Over the past few years I had a Surface pro 3, Surface 3 (my favorite), Surface pro 4, Surface pro7 and Surface go (in order). Also have a Steam Deck.
My opinion is that a Tablet is very poorly suited to play keyboard+mouse games, a laptop is much more convenient. What I mean is that you cannot have it confortabvly on your lap neither the inputs are suitable for K+M or older games. You may want to treat a tablet as a portable display with processing power embedded instead of a full blown computer.
That said, I played a lot of games on the tablets using the attached keyboard on a table, pen and finger while commuting around and a bluetooth gamepad on the car. There's a freaking metric ton of fun games to play (including emulation) but I cannot for the life of me imagine playing HoMM3, I can test the game on the Surface go if you want.
I made a thread a few years ago about games with touch support on GOG, let me trying to find it.
The Steam Deck is not that expensive considering the performance diference and a family member, recently bought a used one for less than 250€. After some time to get used to, the trackpad (small touchpad) is actually very decent to play mouse games, the touchscreen precision is crap though (not needed at all).
IMHO, is the best option, by far, to play games. If your need also general computing, then a tablet might also be a option.
A laptop is probably the best choice as a general purpose device.
Some random tips:
The Microsoft Surface line is hard to use without the attached keyboard on some ocasions but the on-screen-keyboard is actually my favorite keyboard of any device I've tried and a pen is very helpfull. I mostly use the tablet with the finger and pen most of the time, without the keyboard attached (finger to type and scroll and pen to point and click).
Other than a pen, a wireless mouse is also decent for playing older games, such as HOMM3. Controller for the newer stuff.
Most of Microsoft surface Pro tablets are very hot. I do not recomend the Pro 3 or older and to be honest, any dual core (Pro 5 and below) is considered very underpowered but the Pro 3 specially due the age, even for browsing the web. On the other hand both the Pro 6 and 7 are quad core but still hot as heck. My laptop has the same CPU as the Pro6 and I run the CPU underclocked to 2.4GHz because anytime the turbo kicks in, so does the fan, and good bye battery. The Pro7 does not turbo without charger connected.
The graphics on the pro 3 are very weak and the pro7 and beyond quite decent (still hot though).
I like the passive cooled tablets but of course, they are not as powerfull. I also prefer the 10" screen instead of 12" on the Pro line. That said, is much easier to create usable custom resolutions on the Pro models. The Pro3 have a screen of 2160x1440 and if a custom resolution is created at exactly half the dimentions, 1080x720 is still good enough to see things and read (on games it saves a freaking ton of battery) while the 10" screen with 1800x1200, one get a very meager 900x600.
Older surfaces are not reparable, keep that in mind. Check iFixit website to see what models are "reparable" because with the age, the battery wears and some batteries do swell, sometimes breaking the screen. Take care on used units, make sure to purchase a good unit, wich maybe a little dificult to find.
The Steam deck input is very configurable, with the provided Steam OS and can enable playing with relative confort a unbelievable amount of games.
Edit: sorry for the very long post and feel free to ask any thing, if you want I can try HOMM3 on the surface Go and check how it goes.
Link for the mentioned thread (not updated in years):
https://www.gog.com/forum/general/list_of_touch_supported_games_on_gog