Relocate Water Heater to Garage - Pipe Size Issue?

We have a 20+ year old house in South FL with a 40 gal. water heater in a hall closet (no drain or pan). I am in the process of remodeling the master bath, which has a wall against the garage. My plan is to install a larger heater in the garage and tap into the bathroom lines right on the other side of the wall.

The house is on a slab, with the pipes coming up from below.
When I did the other bathroom, I want to say that the pipes coming up to the bathtub looked to be 3/4" copper and then they changed to 1/2" but I don't really remember. They may have just been 1/2" up from the slab. I do know that the existing heater piping in the closet looks to be 3/4".

The shower in the master bath back right up against the garage wall, and that is where I plan to tap the lines. Will it matter if the shower lines coming up from the slab are only 1/2". Most water heater connections are 3/4", correct?

If the lines coming up the slab for the shower are 3/4" it seems like I would have no issues...but if they are only 1/2" lines, can I simply reduce the 3/4" water heater connections to 1/2"? The house is relatively small 1800 sq/ft and will have 2 adults and 2 kids (1and 3 years old). Would I have flow issues? Anything that I may be overlooking?

The electrical panel is also in the garage, so that would be an easy hook-up...

Thanks for any advice/suggestions...this is a great community you have here!

You haven't mentioned how many baths you have.
Here is a chart on water sizing.
https://terrylove.com/watersize.htm

Water heaters should have at least 3/4" pipe run to them.
Normally only two plumbing fixtures can be run on 1/2" pipe.
Your washer and your kitchen sink, that's two right there.

We only have 2 baths.

Maybe I will get lucky and the bathroom supply will be 3/4"...

If the hot line for the bathroom is 1/2", it would be fine for a shower and lav.
I normally run 3/4" for a toilet, shower and lav, with 1/2" braches to each fixture.