"Macintosh XL" was a marketing term, basically, and its precise interpretation differs in documentation and differs between different people. In my book, if it is running MacWorks of some version or other, you can call it a MacXL. Otherwise it is a Lisa.
It's not the case that all of your software is Mac software: you appear to have a copy of the Lisa Office System as well.
Anyway, you will need to remove the batteries now, as they are still damaging your Lisa as long as they are fitted. The I/O board does not look great, but I have seen worse. It may be recoverable if you have the skills and equipment for it. The motherboard has probably also been damaged somewhat, as evidenced by the corrosion visible on your serial ports.
A repair journey now awaits you. How do you assess your skill at troubleshooting electronics and carrying out electronics repair? Unfortunately some of this work will almost surely be necessary in order to recover from the damage the batteries have wrought on the I/O board and motherboard (at least).
If you do not possess these skills now, but you have a desire to develop them, one option would be to arrest the damage from the battery leakage and place the Lisa back in storage until you are ready to tackle this restoration project later.
Have you seen
this series of YouTube videos by Adrian's Digital Basement? They may give you a good idea of the nature of the project of repairing your Lisa.
While this computer is absolutely not ready to be plugged into the mains, I disagree with
@MOS8_030 in "The whole setup will need, at the very least, all the capacitors replaced for it to be reliable to operate." While this comment surely only refers to the computer's electrolytic capacitors and the RIFA paper safety capacitors in the power supply (as small ceramic caps like I/O board C4, C5, C6, C7 hardly ever fail), it is very likely that most of the violet-coloured axial electrolytic caps on the I/O board (except for those with corroded legs) are fine, and so are similar caps on the other logic boards. Some electrolytic capacitors in the power supply and a few on the video card may require replacement. The RIFAs should certainly go unless you want to fumigate your Lisa and your bench with noxious smoke. But even an exploding RIFA is unlikely to do much damage.
The real issue to correct now is to remove the batteries and treat the damaged area so that all traces of the leaking electrolyte are gone.
