This might be a DirectInput issue, as Jazz2 was a game made many years before xinput was a thing. But if I don't power on one of my wireless Xbox One gamepads before launching jazz2.exe (with Jazz2+ installed of course), the inputs from my Xbox controller won't get registered at all in Jazz2+. I would then have to exit the game, and power the Xbox controller on again before launching the game if I would like to play this game with a gamepad.

Maybe there's limitations in DirectInput itself that doesn't allow for a gamepad to be initialized after launching games using DirectInput as the controller API?

(I did afterwards do another test, just to check if an initialized Xbox gamepad in Jazz2+ would permanently loose connection in-game after pulling out a battery inside, and putting the battery in again a few seconds later and powering the gamepad on once more to see if the Xbox controller got re-initialized in-game. To my surprise, once a Xbox controller is initialized before launch, if the controller looses connection because of empty batteries, the game still remembers the gamepad after changing batteries.)

IIRC if you press the J key in the main menu, that tells the game to check for controllers again

That mostly did the trick. By mostly, I mean the controller get initialized in the main menu, but the D-Pad of the controller doesn't do anything after that. The rest of the buttons seem to work fine though, although using the left analogue stick for directional buttons is not in my opinion the optimal experience while using a gamepad.

I don't find any info regarding using the J key in the main menu to check for controllers again in the JJ2+ Readme file online though. Could this be added to the section "Features and fixes" maybe?

While talking about the section "Features and fixes", if you ask me, other noteworthy inclusions there could be that the D-Pad of the Xbox controller now can be used with Jazz2+, as well as the Back button on the Xbox controller now acts as Escape. I believe that info can be found under "Latest Changes" somewhere, but it takes quite some time to discover those additions in the changelogs on the JJ2+ Readme page.

I remember before those things were build-in features of Jazz2+, that I had to use other applications to map my Xbox controller while playing this game to get those exact functions that Jazz2+ now provides.

I mean the controller get initialized in the main menu, but the D-Pad of the controller doesn't do anything after that.

I have an internal branch that fixes this that I made two years ago, but the rest of the plus team has refused to test it. Someday.

I don't find any info regarding using the J key in the main menu to check for controllers again in the JJ2+ Readme file online though.

The J key isn't a JJ2+ feature, JJ2 has always had that. I've added it to this wiki page because I don't remember if it's in the game's manual anywhere.

While talking about the section "Features and fixes"

The features and fixes section is definitely not kept in good shape. At some point I want to expand it significantly and reorganize the documentation in general, but in the meantime it would be nice to just crowdsource what that section should look like, similar to how I'm hoping someone will write MLLE documentation someday because it's something literally anyone can do.