If you're adding rake you're reducing trail. You can get that trail back by slackening off the head-angle a bit which would happen if you used a headset with a higher lower stack height. 10mm of extra rake can be compensated for by about 1.5 degrees more slackosity of the head angle which you would probably get by about 10mm extra lower stack, making your TT imperceptibly non-horizontal. But it will probably ride fine though a little differently if you just go with less trail.

Equal trail but achieved with slacker head and more trail will make the handling mostly the same, but you will have a bit less wheel flop. This is often how tourers are built because a bit less wheel flop is considered desirable if you have bags on the front.

I also kind of think a wider handlebar means you want more trail. Modern MTB frames have really wide handlebars and loads of trail and feel "normal" to ride.

If you post actual numbers of fork offset, head angle and wheel-base I can attempt some math. But long story short it will probably be fine and, if not, adjusting the lower stack is an option. This parameter often gets randomly adjusted when people buy new headsets anyway.