You don't stick a screwdriver anywhere. On the front of the pump there's a black hex thingy and you unscrew that, pull outwards to engage the rotor and spin it like that. That pump is very old and could well be beyond repair. Good luck with all that, as the access to the front looks poor.
You could loose up the 22mm nut on valves on both side, just enough so the the pump can be turn over for access and test it. Be ready for escaping water.
Slacken the nut only a half turn, the joint will still hold together and allow you to turn the pump. Your hot water tank contents will not be affected in any way.
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