Pro: It's a benefit of my previous employment and easy to apply for. It could help if it takes a while to find work. I just got laid off so maybe the whole industry is slow too.
Con: I'm not comfortable "gaming" the system with terrible resumes and interviews, and if I got a great offer right away, I'd take it.
OP, I applaud your concern about gaming the system. However, I don't think anyone who is actively looking for work and says "if I got a great offer right away, I'd take it" would be doing anything wrong, even if they were hoping for a longer break.
Also, as you allude to, I highly doubt given the tech landscape right now, and the multiple rounds of interviews you're likely to go through, that you'll find a great offer in a few short weeks. And if you do find it, it's pretty common to negotiate a start date that's a few weeks out. That's easily two months even if you apply tomorrow for a great job you end up getting. Frankly, if you want a job three months from now when your lease is up, you
should be looking now.
My advice: take unemployment, apply for jobs that interest you, realize that it might take months, and enjoy those months! Maybe set up a schedule where you spend X time in the morning X number of days a week looking and applying, then put it out of your mind and go enjoy not working. Spring is a great time to just get out and explore all the things you've been not doing since you've been glued to a computer screen for the past few years.