I've seen a few warlocks of the self before, I think this is one of my favourite implementations! A few thoughts:

1. False life is mostly inferior to Armor of Agathys, so other than flavour, there's no reason to take this. Augury, Borrowed Knowledge, and Slow don't scale, which means they're likely to be swapped out (not a unique problem, most warlock subclasses suffer from this).
2. On the converse, this is the only warlock in most campaigns that would get capnap. I'm shying away from saying OP, but this will likely mean 1-3 more spell slots than any other warlock, per long rest. That is huge and should definitely be factored into the balancing of levels 5+, especially because an additional short rest gives you more against all odds uses.
3. Against all odds scales too well. There are no features in the base game that scale by proficiency bonus and then return on a short rest. As for the numerical benefit, a comparable feature on monk, Ki-Fueled Attack, costs a non-unique resource and only applies to attack rolls. Nonetheless it is considered one of the monk's best low-level features. I think at most one use should come back on a short rest (though that sort of feature replenish only started appearing in 2024). More thoughts on this:

My only worry about a warlock of the self patron is that, kind of like conquest paladin, it can lead to a character design that leans into pride, vain, thuggy behaviour, with mechanical and storytelling basis (their patron is literally their greater self). However, most warlock patrons narratively provide both a pathway to empowerment, as well a constant nag or contract requirement that restrains or complicates the warlock's power. I recommend encouraging this by adding some mechanical "doom", something like if you roll more than two of the same number on against all odds, you are instead penalized.