System run out of application memory

To add to your computer issues and what @BobHarris has mentioned - Lack of Space on the 256 GB SSD Drive

Report says >> macOS Ventura 13.2.1 (22D68)

Current version of Ventura is Now at version 13.6.9

Report says >> Time since boot: About 49 days

You will have some serious house cleaning to do even before updating

There are 2 reasons for the "Your system has run out of application memory" dialog box. A. Your boot disk has very low free storage, and macOS cannot create page/swap files to offload virtual memory contents to disk. Depending on how much virtual memory is being called for, anything under 50-100GB of free storage may trigger the message. Apple menu (upper left corner) -> About This Mac -> More Info... -> Storage (scroll down a bit) -> Storage Settings... B. A process (or set of processes) has asked macOS for excessive amounts of virtual memory address space. In order to keep track of the virtual memory address space, the kernel creates virtual memory page tables. If there is a memory leak (process asks for a virtual address range, forgets to give it back, asks for another range, forgets again, wash, rinse, repeat), eventually there are so many page tables created there is no memory left for applications, and you get the "Your system has run out of applications memory". Look at Applications -> Utilities -> Activity Monitor -> View (menu) -> All Processes -> Memory (tab) you can see what processes are using lots of memory. Many of these processes will be background agents and daemons used to provide many of the macOS services, as well as your applications. Also keep in mind that each web browser tab will be a separate process running its own Javascript. If you have lots of browser tabs open, or if one of the browser tabs running Javascript with a bug in it, it is possible these browser tabs will add up to a lot of virtual memory demands, but no individual tab will look all that big.

It sure looks like a Firefox problem. There's an easy way to test this. Restart. Then use Safari. If you don't experience the problem, then you've identified the cause.

You should probably also update your operating system. I can understand people not wanting to run whatever the latest, buggiest version of the operating system might be (Sonoma today, Sequoia in two days). But there's no reason to run an old version of Ventura. At least update to the latest version of Ventura.

This part from the Kernel Panic log seems like it may be a hardware issue:

 panic(cpu 4 caller 0xfffffe0012bba74c): "i2c3::_checkBusStatus SCL is

            stuck low;

For the extreme memory consumption, a web browser would be most likely the source of the problem since 17GB of Swap has been used which is excessive.

Give etrecheck Full Disk Access before running.

What all devices do you have plugged in?