There is never enough extra room inside a modern plastic housing power strip for a relay large enough to handle the 15A of a typical power strip. You could look for a large expensive metal power strip with like a 4"x4" or larger end profile and hope it has enough room inside. The most common solution is to make an external housing and wire it to the power strip via a heavy gauge wire like this person did.
To get the momentary switch to do both the on and off triggering you need a step relay instead of a latching relay. This one will do the job.
The data sheet is a bit lacking but I believe you would use the 240VAC wiring example for this 120VAC stepping relay. The diagram is for a DP unit and this is a SP unit so terminals 3 & 4 won’t be on this relay.
The hot line from the AC cord (black) goes to terminal 1 and terminal 2 goes to the power strips hot line. A neutral wire (white) needs to connect to terminal A2, and the momentary switch connects between A1 and the hot line.