The release you've signed is pretty normal, nothing to really worry about (Unless they've done anything illegal, in which case you're not obliged to adhere to the release but I don't think that's the case).
Just get back on the horse. This happens to the best of us.
But if you have some funds to tide you over I wouldn't recommend jumping onto the first horse you find. Go for some fun pony rides first.
Most people have a list of "minor aspirations" that are constantly deferred due to the pressures of work. Now's a good time to achieve those. Much better than going on vacation, which I believe is a bad idea after a lay-off as your mind constantly replays what has just happened and you come back to the real World having achieved nothing but self-criticism.
They don't have to be World-changing aspirations, just something to achieve on your own schedule. For example I kept reminding myself to schedule time to take photos of some derelict local buildings as I passed them every morning en route to work, but I never found the time and eventually they were demolished and rebuilt as anonymous apartment blocks. I wish I'd taken one morning off work to photograph them.
so true
I agree, it can be a full time job and you should take the job search seriously. BUT it puts you also a very needy state if you are not careful. If you apply 24/7 30 days in a row, I am not sure if you will get that more job offers than if you just spend, let's say 2-4 hours every other day. It's more about being efficient and creating many job opportunities while spending little time on the actual job hunt.
Reason: If you are in a needy state everybody can feel, smell and see that you are needy. Actually, they don't need to see you in person, your voice and the chosen words on a phone call disclose your level of neediness already. If you spend 24/7 for job hunt, you MUST be needy or you will get needy at some point. And who wants to hire a needy guy (who just got fired)? Nobody.
Besides, the activity of applying (writing always the same emails, doing minor tweaks on your CV again and again, doing interviews with HR folks asking about your weaknesses, getting rejections or no responses) is not really fulfilling at all, therefore I suggest in the other answer to spend also some time on personal projects, they give you back your state and let you be perceived less needy.