My recommendation would be to apply to as many positions as you can, but steel yourself to the fact that you may not hear back from any of them. I'd also recommend exploring if you can push graduation back by a year (assuming funding would cover it and you have legit research to do), or if you can pick up part time lecturer, post doc etc type of positions for the next year. IMO, job prospects for software engineers will likely start improving in the last quarter of 2023 and be much better in 2024. So I'd plan to tough it out till then.

I do empathize with your position and wish you luck :) I'm ever grateful to the first manager who hired me. He changed my life forever and that of my family.