OP. It sounds like you have had time on your hands now it's the summer, away from the school gates to think about things.
We made a very similar decision (top independent and outstanding state) a few months back when the fallout from COVID started to hit. Plus, exactly, as you are now, being away from the 11+ chat gave us time to see the 'wood through the trees'. However, we had a state place. Before we decided, we checked the online provision of the state with other parents and it was on par with the local private school ie. lessons all day. We were lucky as one parent had a child in both so was able to give us accurate comparable information.
It sounds like the state secondary online provision is good. Even so, hopefully this situation will last no more than a year so that would become irrelevant anyway. It does sound like your DC will work will in any school, but you just need to deal with what you have in front of you now. Get your DC on the waiting list at the secondary ASAP (although it sounds as if you already have? If so. Which waitlist number are you?). You have nothing to lose.
Your DC will likely start at the private school in September (as others have said, you will have paid for a term in any case), then see what happens. It may be by that time you'll be able to see more clearly how Covid will affect your family situation and you may feel more comfortable with your initial decision. However, if the children go back to school as normal, it will be harder to move your DC once they start and you may have to come to terms with keeping them at the private school. You will find a way, I'm sure, particularly if they are enjoying it (which undoubtedly they will!).
The best case scenario is if a place comes up in the next few weeks at the state school so your DC can start immediately in September, then you can write off the terms fees in your head as at least it's not £150k+. However, this may be unlikely at this stage, particularly in the current climate.
Good luck. Please do PM if you would like to chat further. And please keep us posted as to what happens.