What is the latest OS I can use with my MacBook Pro (Retina, 13-inch, Late 2013?

macOS Big Sur is the latest possible.

See the following from Identify your MacBook Pro model - Apple Support

MacBook Pro (Retina, 13-inch, Late 2013)

Model Identifier: MacBookPro11,1

Part Numbers: ME864xx/A, ME865xx/A, ME866xx/A

Newest compatible operating system: macOS Big Sur

To upgrade to Big Sur or earlier, see instructions in How to download and install macOS - Apple Support

Be aware that if you upgrade to Catalina 10.15 or later you will also need to update any non-Apple 32-bit apps. See: https://www.stclairsoft.com/Go64/

or

 https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html

I'm not aware of any Adobe Creative Suite products that will run in macOS Catalina or later. See: https://helpx.adobe.com/x-productkb/global/fix-macos-64-bit-compatibility-errors.html

Big Sur.

Read How to download and install macOS - Apple Support. Scroll down to Big Sur 11.

I think with the Adobe products, you're going to be stuck between a rock and a hard place.

I don't know if the main applications for CS4 are 64-bit, but I think that even CS6 has 32-bit installer and activation components that won't run under Catalina or Big Sur. Adobe no longer supports CS6, so I'm sure that goes for CS4.

If you go to subscribe to one of the Adobe Photography Plans, you'll probably find that the system requirements call for you to have one of the most three recent versions of macOS. The release of Sonoma caused Big Sur to drop off that list. If Adobe hasn't already stopped supporting Big Sur, they soon will. That might mean that you must "jump through hoops" to get unsupported versions of the Adobe applications that will run on Big Sur (but that will get no further features or bug fixes). It might mean that you can't get the Adobe applications at all. You need to ask them.

Just double-checked. The Photoshop requirements as of this instant say that you need macOS Big Sur (version 11.0) as a minimum; that macOS Ventura (13.4) is recommended; and that "Installation is blocked on v10.15.x." – the current version won't even install on Catalina.

Any day now, the minimum OS may change to Monterey, and the recommended OS may change to Sonoma.

https://helpx.adobe.com/photoshop/system-requirements.html

I didn't look up the requirements for Lightroom and Lightroom Classic, but expect that they would be similar.