Error 2002F and problem with Mac update

So for the past 2 days I've been looking at what to do online and nothing has worked.

I am trying to delete and remove all my information so that I can give my MacBook pro to a family member, so it will be clean and new for them.

I was running Mojave, I've backed everything up to TimeMachine and moved onto my new device so went into Recovery with CMD R. It took me to internet recovery mode, choose a wifi connection and log in. Brings me to Error 2002F. I've tried the solutions about changing DNS and it hasn't worked. I've even plug in Ethernet cable, however for the recovery mode it doesn't recognise it despite working normally before going into recovery mode. I've made the ethernet default, I've reset the NVRAM. So I'm able to go into Recovery to delete everything.

Also I thought about installing to new OS, Big Sur. I go to download and install it downloads, restarts and upon restarting I get a start-up error. So I'm in a Limbo.

I can use my computer by restarting and holding Option and clicking on my HD. I can't click on Install Os or Os as it just goes into the start up error symbol.

The way most solutions have to bypass this is with internet recovery and CMD R, however that isn't working for me with my 2002F error and the fact the recovery mode isn't recognising the cable.

I thought this would just be a simple thing to be able to hand the computer over as a clean slate with all the memory and all my items deleted, but it's turned into 2 days of pain and trail/error.

I admit I'm not well versed with the DNS's and everything for that to work, but I thought the cable would bypass that.

Any suggestions or people who have had a similar loop to fix both problems.

Would be happy just fixing one of them though first. Either error 2002F or if I can install an upgrade properly without having to use CMD R if it's not working.

I read about putting the new Os and install on an external HD, will that work for me in this case?

Thanks Joe