What’s the timelines? Pool went in before the ‘side’ extension or after?
Do you know the size of the excavation that occurred for the pool, and ground conditions?
Is the new extension to be 1 or 2-storey?
You may be able to do a piled (screw vs percussion) foundation to completely remove the need to excavate, other than for a foul pipe if there’s need for drainage. You’ll need geotechnical survey doing by the foundation contractor or independent to see if that’s an option, plus you’ll need to know what services lay beneath, historical records for mains sewers / gas / water and so on.
I’d be asking a ‘pool expert’ if you’re better off emptying the pool during these works, or half emptying it, or leaving it full etc. That will likely be a good SE, one who’s done pools before. I have a very good SE I can share details of who’s very well versed in ICF / pools / basements, PM me if you get stuck.
For a covering, do a good job as you don’t want any damage to the pool whatsoever. 4x2 timbers across the width and 18mm OSB sheets to cover the pool. Make some uprights at each corner and midpoints as necessary with hazard tape strung between them to act as a guard rail, and a BFO sign saying not to walk on it and swimming pool below etc.