The other controller configs shared here had some buttons mixed-up or non-functional, and there were zero solutions to address the KB&M icons and button prompts, so here's a simple "all-in-one controller mod" for you.

Marc Ecko's Getting Up - Xbox controller mod v1.0[drive.google.com] – contains modified bindings; for Xbox 360 controllers and XInput wrappers
Marc Ecko's Getting Up - Xbox controller mod v1.0-alt[drive.google.com] – contains unmodified bindings; for some setups with Xbox One/Series controllers inexplicably incompatible with the regular version due to broken mappings

※ I'm not entirely sure which version you should go with if you're XInput-wrapping the controller via Steam Input (or maybe have Steam Input enabled for native XInput controllers), but probably try the alternative version first.

Be absolutely sure to also install a fix by misticjoker! It replaces the button prompts represented using text characters (i.e. (A), (B), (X), (Y), etc, like you can see on the screenshots below) with the actual Xbox icons + it restores the OG Xbox controls screen in the settings menu as well.
https://steamproxy.net/sharedfiles/filedetails/?id=3135657757
There are also DualShock 4 Controller Mod (ENG/RUS) by ARTONE1922 & a version for additional languages (FRE/GER/ITA/SPA/JPN/BRPT) & general addendum by misticjoker available, too, which feature the actual PlayStation glyphs during gameplay and restored PS2 controls screen from the get-go.
https://steamproxy.net/sharedfiles/filedetails/?id=3132010719
https://steamproxy.net/sharedfiles/filedetails/?id=3084117172

Simply overwrite the files in the game's directory with the ones included in the mod's archive.
※ You can locate the game's installation directory by right-clicking on the game in the Steam library, then selecting Manage -> Browse local files.

UI button images and the controls screen:

In-game controls tips and the unlockable moves screen:

• Since the game has no proper XInput support, LT & RT triggers share the same axis, which means that pulling a trigger when the other one is being held will cancel both of the inputs.
  Thankfully, there are few to none gameplay scenarios when you'll actually need to hold both LT & RT. The only such situation that I can think of is... doing the Flamethrower move while trying to maintain lock-on on an enemy.
  
  
• I've no clue how to invoke the actual button icons for the controls tips pop-ups like it's done in the console versions, so the buttons are instead represented using text characters within parentheses: (A), (B), (X), (Y), etc. Note: rectified via a fix by misticjoker.
  
  
• This mod won't restore the DirectInput-exclusive rumble feature, you'll have to use a DirectInput-compatible controller or a wrapper (and remap the controls on your own) to get the rumble working.
  
  
• In case you'd like to remap the controls to better suit your taste, binds_pc.cfg (regular ver. only) has been comprehensively labelled to aid with that task, and the strings.str files only require you to tweak the lines #567-574 and, optionally, lines #2002-2019.
  
  
• This mod is also compatible with the non-Steam / physical versions of the game.
  
  
• This very mod but without the bindings file was also reposted here. So in case you've obtained it there, all the info from this page still applies to it sans the aforementioned lack of any bundled binds_pc.cfg.

2023-02-23: Added an alternative version bundled with unmodified bindings for anyone experiencing incorrect/bugged mappings when using the regular version.
2024-01-10: Linked the fix for this thing by misticjoker & DS4 version by ARTONE1922.

• Asbra / novocain for the GettingUpTool[github.com](thread), which was used to fix the alignment of several button textures that came with the game
  
• I AM GROOT / vroomsim for the original Xbox 360 controller bindings that were referenced for this mod
  
• ARTONE1922 / Жиган Лимон for figuring out the gameplay icons, console controls menu, and creating the DualShock Controller Mod
  
• misticjoker for making an addendum to this mod and thus completing it, and also for putting together a DualShock version for additional languages & giving it an addendum tratment as well
  
• And everyone who reported incorrect input mappings with Xbox One/Series controllers