Incorect reflection on a flat surface (mirror)

Hello all
I am building a Victorian drawer with a mirror attached to it and because I didn’t want to create a whole environment just for the reflection I’ve decided to do the reflections/environment with a hdri map/dome light.
Now I have the problems that the reflection in the mirror is looking pixelated and appear much bigger than it would in real live. On a chrom ball which I created for test purposes everything looks ok
I understand that the resolution of the map is possibly to low because the mirror is only reflecting a smal portion of the map but is there at least a way to correct the size issue? or is there even a patter sollution to
do the reflections exept for building a whole enviroment?
An idea or tipps on how to make the reflection look correct on a flat surface via a hdr map?

thank you for any help or suggestion

Tile the map?

This is a long standing request I have with VrayHDRI: Dome light with ground projection: Environment above horizon is incorrectly scaled - Issues - Chaos Forum

Nothing you can do, sadly.

Map it onto a sphere and use trace sets so that it’s only visible to the mirrors reflection.

I’ve tried tiling the map but because I want to also crate a turntable animation this is not really an option. It works or a single shot put not realy in an animation.
To put the map an a sphere or cylinder is also not giving me a good/sharp result and I don’t have access to a really high resolution enviroment map of a victorian style interieur.
I found now a free victorian livingroom model on the internet and i will try to render my drawer in that modeled enviroment.
Maybe this will give me the result and the mirror reflection I’m looking for.

Thanks everyone for the feebacks.