The 2-300 euros budget is really going to limit your choices. The trade-off is always about what part of the bike gets your money.
Do you get a better frame that a brand makes, only bottom of range with lesser parts, or do you get a bike with shinier parts (hydraulic discs/better groupset/carbon forks) and a heavier frame?
You can always get a few low cost contact point upgrades in a year or so that really will make it a new ride by absorbing road shock and dropping about 1.5 - 3kg's:
But a frame upgrade that's lighter and absorbs more vibration, or a groupset upgrade that changes gear more smoothly, brakes better and lasts longer are major things.
The manufacturers could put these parts on up front for a few dollars more, but it would cannibalize their more expensive (and highly profitable) bike market.
Whilst this doesn't answer your question about what bike, i hope it helps with making the final decision once you've decided on mountain or gravel bike.
Btw, gravel bikes are 3-5kph faster than a mountain bike on the road, 1-2kph faster on clean gravel, but 5-10kph (or more) slower on gnarly single track or downhill as shown on the youtube GCN channel.