dabac

I’m not entirely certain what you/the mechanic are actually talking about here.
Usually when you get a sequence of spokes breaking like that, what you have is a bad build. Spoke tension not high enough and/or not even enough.
The consequences of that on the spokes is kinda contagious, so a loose rule-of-thumb is that once a wheel has had three spokes broken w/o apparent cause, it’s time to fix them all.
One way of doing that is of course to get a new wheel.
However, if that wheel is in the same price range, there’s no guarantee that the spoke tension would be any better. For a better chance of a reliable ride, ask the shop to go over the wheel BEFORE you start riding on it.
What did he mean by ”tire rim”?
No need to say that. There’s only one kind of rims on a bike.
Did he mean you need a new tire too?
If so, why?
While I suppose it’s possible to remove and remount a tubeless tire so many times that it becomes a loose fit and stop sealing up, I haven’t seen any guidelines on max number of remounts.
And there’s no reason to assume that the rim is afflicted either, if the root cause is a bad build.
From only having your post to go on, what I’d have done is rebuilt the wheel with new spokes. Kept the hub, rim and tire. Might not save much money compared to buying a wheel, but that way I’d know I’d gotten the parts causing the trouble sorted out.

Now, maybe the mechanic has spotted something else that makes a rim/wheel replacement a sensible thing. Maybe you’d be better off with a wheel that’s stronger overall. Maybe there is other damage. But generally there is no need to replace a rim for a build quality issue.