I currently have BTCs in my BitPay wallet and I cannot transfer it to my local wallet due to the very high transaction fees being required (more than $20 currently). Is there like a website or an application that I can use for me to send my BTCs by using a relatively lower fee? I do not mind if the transaction would take days; what matters is that I receive it on my local wallet.
BitPay wallet is a custodial wallet, so you can neither set nor customize your fee rate, i am sure BitPay has their own fixed withdrawal fee that you must use when withdrawing funds, just as it works on centralized exchanges. If you cannot pay the withdrawal fee on that custodial service, you have to wait for fee rate to drop, but take note that not your key, not your coins.
Even if price of BTCs reached an ATH of ~$68,000, tx fees were relatively lower during that time.
BTC tx fee is not determined by the price of BTC.