I have only seen something like that for 2x4 and for 4x4.
See: Simpson Deck Post Tie DPTZ
The DPTZ Deck Post Tie products are used to attach 2x4 (DPT5Z) or 4x4 (DPT7Z) vertical posts to the side of stringers, rims or other wood members.
2x4 Deck Post Tie
4x4 Deck Post Tie
You could ask your "engineer" if you can make your own 2x2 tie with some strapping.
If you gave us a better idea of what you are trying to do, maybe we could come up with a better solution than a bracket that probably doesn't exist.
Opinionated aside: You would think that some lags or structural screws would be sufficient.
Why I think that and also the likely reason that they don't make these brackets for 2x2 (which is what you are talking about) is that the 2x2 is probably weak enough that a bracket is pointless. By that, I mean that the force needed to pull out lags or structural screws would snap the post before pulling out the fasteners, making the bracket pointless.
That and I can't imagine where a 2x2 would be counted on as any form of structural member anywhere but a balustrade.