I want to try the Ubuntu server without installation, but when I reach the step of booting from a USB stick, it shows me "Try or install Ubuntu server" in the same choice as the below photo.
When I chose that choice it installs Ubuntu:

I want to try the Ubuntu server without installation, but when I reach the step of booting from a USB stick, it shows me "Try or install Ubuntu server" in the same choice as the below photo.
When I chose that choice it installs Ubuntu:

Boot up with the live server ISO image, you can choose "Enter shell" from the [Help] menu on top-right:
This is about as much as you'll get on a fully installed Ubuntu Server system. No desktop, no GUI, and a shell right away (except on an installed system you'll have to log in with your username and password). This environment comes with a minimal set for installing Ubuntu Server, and additional software can be installed online as usual with apt install.
This is also useful as a recovery environment to repair or modify an offline Ubuntu Server system, although I personally prefer ArchISO for this purpose.
If your computer is powerful enough, you can install Ubuntu Server into a virtual machine (use for example VirtualBox). A basic Ubuntu Server needs less CPU and RAM than Ubuntu Desktop, so you are likely to succeed according to the advice by @matigo.
It is also possible, and actually quite easy, to install Ubuntu Server into an external drive, a fast USB 3 pendrive or even better an SSD connected via USB or eSATA.
You can extract and clone a compressed image file into the target drive. Please notice that the whole drive will be used, so avoid writing to your internal drive. This method is described at this link to a thread at the Ubuntu Forums. Before using the method, please read the whole thread. I suggest that you use the Jammy version,
cdimage.ubuntu.com/ubuntu-server/jammy/daily-preinstalled/current/
[Of course] it is also possible to use the installer and install Ubuntu Server into an external drive. It provides more options, but is also more complicated.