Please Help! My MacBook Air will not boot. I get to the Apple, and then it keeps going back to the apple icon. I've tried all the startup commands on Apple support. Bought a Thunderbolt to connect to iMac but don't know what to do next. Please help, I'm so frustrated.

I have an older Macbook Air (circa 2019). It still runs on Sonoma, because it ran out of memory for me to update. I tried all the tricks to make more room and I was able to update to a newer version last year. I don't use it for much other than online teaching, powerpoints, and the word processer. I went to use it a week or so ago and it was doing some sort of update. So I just went my iMac M1 running Sequoia. When I went back to try to use my laptop it just boots up to the apple icon. It prompts me to select the startup disk, I do, and then enter the password. It restarts and takes me back to the same page. I've tried Recovery, but I don't have enough room to download the newest version. I went to the Apple support page. I've tried the Recovery and repair. I've tried all the different options it tells you to try. Nothing works. I did get a Thunderbolt cord and connect it to the iMac and was able to get the disk utility to pop up and it has all my data on it. I tried finding out how to restore from the iMac, but the instructions confuse me. I just want my laptop to start up. I can take it to a shop but it's such a pain. I do have an external hard drive but it hasn't been updated. Could I update it with a copy from the Thunderbolt and try to recover from Time Machine? I'm not all that computer savvy I just google everything, but I don't want to fuck everything up. I should be backed up on the Cloud too. Any advice would help. If I need to update the laptop, I can. It's just that really I only use it for basic things, and watching movies when I'm overseas using a VPN. I don't game or a lot of software (that I know of). Thanks in advance.