how to access BTC sent to different addresses generated by same private key??

Sorry if anyone has ever asked this before but I'm not turning up anything close when I search.

I generated my own private key by rolling dice, this is in hexadecimal form. Then using bitaddress.org (offline of course), I generated a public address in P2PKH format (I think, since it starts with a 1). I sent $10 of BTC to that and confirmed it on a block explorer. As a test, I have imported the private key into a hot wallet and successfully accessed my $10 and sent it to another address. Hooray, I feel so smart...

Then I entered the same private key onto my hardware wallet (completely offline), which generated a new, different public address for me, in P2SH format (I think, since it starts with a 3). I sent $10 to it and confirmed on block explorer.

What I don't understand is, without the hardware wallet (say I lost it), how would I access any funds sent to the P2SH public address? How do you access BTC sent to different addresses generated by the same private key?