For my dialogue tags, I use the word "says" rather than "said" whenever a character speaks and responds, for example:
"What do you want for dinner tonight?" Mary says.
"As long as it's not meatloaf again, I don't care." John says.
Is this grammatically correct or off?
Any stylistic decision is a valid option that can be explored. You don't say what you are trying to achieve, so I make assumptions why you are even asking the question.
My assumptions: You understand grammar, and the novel is in past tense.
Is this grammatically correct?
No. It is not correct, it is grammatically 'off'.
It reads like slang, like the voice of an uncouth narrator. I would expect the rest of the narrative voice to support the characterization (or whatever stylistic conceit it represents), or it will just look like a grammatical mistake.
There is a broader discussion about developing a narrative voice, how does he speak, does he use proper grammar. How formal or intimate is the narrator towards the reader, and what social cues is this narrator using to bias us.
In this question: Switching from past to present tense to increase narrative speed?
The OP says that German allows for an effect where switching from narrative past tense to present tense creates a sense of time speeding up, specifically using an emergency as an example.
I have explored this in English. My feeling is still as I wrote above. It feels like a narrator who reverts to slang and poor grammar when they get excited – not a change in the reader's perception of time.
However, this under-rated answer in that same question provides an example from a John le Carré novel. Switching into present tense creates a sense of suspended time where everything is happening at once, and yet time stands still. The protag is emotionally distant. Events are observed in real-time but have no impact or importance, as if they happen routinely on an endless loop. The scene is a spy observing his neighbors, scanning for something out of place. The alienation of the strange switch in tense seems perfect in this context.
One of the problems is possibly that English has multiple types of present tense, each with a slightly different shade of information about time:
In English, present tense is not just 'right now', it's 'always', and 'forever' too. In some contexts it is 'always up to now'.
"What do you want for dinner tonight?" Mary says every night at the same time.
John says nothing. He knows it will be meatloaf. It's always meatloaf.
When the narrator imitates spoken English, present tense now includes "sometimes", "just this one time", and poor-grammar past tense. We are losing objective information and just getting a voice.
I think these other shades of present tense can be jarring within a narrative where the reader is already suspending disbelief to follow story-time. Some people find it unacceptable, like it is breaking trust with the reader or making sudden clown faces.
For me it is just another narrative voice. I perceive it as authorial information about the protagonist's current state of mind, like when... punctuation... is used... to force... time... to breathe...
It's not thaaat effective, and borders on annoying, but I understand what it's trying to do.
The John le Carré example shows it can be subtle and effective.
If the events of your story have happened in the past and you tell the story in retrospect, you narrate in past tense and use said.
Example:
John was sitting on the sofa when Mary came into the living room.
"What do you want for dinner tonight?" Mary said.
"As long as it's not meatloaf again, I don't care," John said.
If the events of the story happen now and you tell the story as it unfolds, you narrate in present tense and use says.
Example:
John is sitting on the sofa when Mary comes into the living room.
"What do you want for dinner tonight?" Mary says.
"As long as it's not meatloaf again, I don't care," John says.
Note that the rule in English is to replace the full stop at the end of a quoted speech with a comma, when a dialogue tag (such as he said) follows.
"Said" is past tense, whereas "says" is present tense. Unless the rest of your novel is in present tense, using "says" would be grammatically incorrect, and you should use "said".