Solid answers by user6726 and DaleM answer the first part of the question ("Is this true?"). This answer addresses the second part of the question:
Hypothetically if a Shari'a country also has a freedom of religion
right (without a restrictions clause) how would the conflict be
resolved between the two?
The death penalty is generally reserved, in places that have it, for apostasy to conversions away from Islam, rather than simply adhering to a faith other than Islam by a person who has never been a Muslim. Apostasy is conceptually similar to the secular crime of treason (which is also punishable by death), in that it can only be committed by people who owe allegiance to the sovereign against whom treason is committed.
Islamic law recognizes the right of "people of the book" who have never converted to Islam, including Christians, Jews, "Sabians", and in some interpretations, certain other faiths, to engage in the free exercise of their religions on a subordinate basis to an established Islamic religion in places subject to Islamic law. Not all religions are entitled to this deference. Some relevant sources in Islamic law arguably also reserve for god rather than men, the task of punishing people for not being Muslims:
Several verses in the Quran are commonly understood as identifying the
Jews, the Christians, and the Sabians as People of the Book. Thus for
example Sūrat al-Māʾida 5:68–69, which mentions these groups along
with the Muslims ("the believers") as being safe from fear and grief:
Say, ˹O Prophet,˺ “O People of the Book! You have nothing to stand on unless you observe the Torah, the Gospel, and what has been revealed
to you from your Lord.” And your Lord’s revelation to you ˹O Prophet˺
will only cause many of them to increase in wickedness and disbelief.
So do not grieve for the people who disbelieve. Indeed, the believers,
Jews, Sabians and Christians—whoever ˹truly˺ believes in Allah and the
Last Day and does good, there will be no fear for them, nor will they
grieve.
Sūrat al-Baqara 2:62 is similar to this, but there is also a verse
(Sūrat al-Ḥajj 22:17) which lists the same groups in another context,
that of how God will judge them on the Day of Resurrection, but now
adding two more groups to the list:
Indeed, the believers, Jews, Sabians, Christians, Magi, and the polytheists—Allah will judge between them ˹all˺ on Judgment Day.
Surely Allah is a Witness over all things.
The last named group, "the polytheists" (the mushrikūn, lit. 'those
who associate'), are the opposite of the first named, "the believers"
(the Muslims). What is less clear, however, is the status of the
groups mentioned in between, who now also include the "Magi"
(al-majūs), that is to say, the Zoroastrians (who are named only once
in the Quran, in this verse). This was a matter of dispute among
medieval Muslim scholars, who questioned whether the Zoroastrians had
a clear prophet and scripture, as well as whether their doctrines on
the nature of God and creation were in accordance with those of Islam
and the other religions recognized as having received a revelation.
Ultimately though, most Islamic jurists granted the Zoroastrians
partial status as a People of the Book, while still disagreeing on the
extent to which legal privileges such as intermarriage with Muslims
should be allowed.
From the Quran, 98th Surah Al-Bayyina - the clear proof, those who
reject the truth from among the People of the Book and polytheists are
described as the worst of all creatures, and are destined for hell.
Similarly, some faiths in the Middle East and South Asia with some overlap with Islamic views, that are a stretch to consider Muslim in a rigid or fair minded evaluation, are sometimes deemed as a matter of tolerance and religious convenience by local authorities as sects of Shi'ite Islam, for purposes of religious toleration.
Countries in which Islamic law is enforced by the government typically enshrine it as an entrenched principle of their legal system, similar to the status of the U.S. Constitution in U.S. law, which is supreme over all other secular laws, domestic and international. This was done, for example, in the pre-2021 constitution of Afghanistan (before the Taliban regained power) and in the drafting of the current constitution of Iraq.
So, the most obvious way, although not the only way, to reconcile freedom of religion found in a constitutional right or human rights treaty of a country, and the requirements of Islamic law, in a country where Islamic law is the supreme law of the land, is to allow freedom of religion as fully as possible consistent with Islamic law's requirements.
In that approach, Muslims are not free to cease to convert away from Islam, or to otherwise engage in blasphemy. But "people of the book" are not required to convert to Islam, and differences of opinion about Islam that don't rise to the level of blasphemy such as those found in different schools of Islamic theology should be tolerated.
A historical example of how this notion of religious freedom could play out in practice is the effort made by Muslim communities in France during World War II to hide and shelter Jews from the Nazis, without treating them as genuine converts to Islam for their own religious law purposes, even though the Nazis were deceived into believing that the sheltered Jews were really Muslims.
Also, the death penalty that is justified for apostasy under many interpretations of Islamic law, or even any other particularly harsh penalty is not necessarily required under Islamic law, even when members of a religious faith are not "people of the book" with limited religious freedom under Islamic law (who may therefore be punished for practicing their faith in Islamic law). This is true even though an Islamic leader may be justified in conquering people of these faiths in order to convert them under Islamic law.
The history of the Islamic world reflects many instances in which people who are not people of the book have been tolerated by Islamic leaders in light of practical realities and considerations, even though Islamic law did not demand their tolerance.
In the same vein, while Islamic law does not forbid polygamous marriage, a couple of Islamic majority countries have forbidden it as a matter of secular law. These countries concluded that it is not inconsistent for secular law to ban conduct for secular reasons even when it is not a violation of Islamic law to do so, in much the same way that Islamic countries still have traffic laws even though Islamic law does not forbid driving though stop signs or going faster than a posted speed limit. As applied to the freedom of religion, while Islamic law does not require accommodation of the faiths of people who not "people of the book" it also doesn't affirmatively require that Muslims persecute such people in most cases (except some kinds of blasphemy).
So there are approaches to interpreting Islamic law that can afford considerable substantive freedom of religion to non-Muslims, and to different kinds of Muslims within non-blasphemous Islam, even though it is not as expansive a view of freedom of religion as the U.S. First Amendment provides - particularly as applied to Muslims who want to convert to another faith.
Another final point is that the majority view in Islamic theology is that adherence to Islamic law and the Islamic faith is a matter of overt actions and not internal sincerity. The leading view is that if you fulfill your outward religious duties like praying five times a day, observing Ramadan, honoring Islamic dietary restrictions, and not making public blasphemous statements, that you are still a "legitimate Muslim in good standing" so to speak. This is true in the leading view, even if in your heart of hearts and internal monologs with yourself, you have deep doubts about Islam or even actually don't believe that God exists at all. Theologically, in Islam, the leading view is that actions speak louder than words or thoughts.
