Add this to your hardhat.config.js, after accounts:

 gasPrice: 8000000000, // default is 'auto' which breaks chains without the london hardfork

Full entry:

  matic: {
      url: "https://matic-mumbai.chainstacklabs.com",
      accounts: [PRIVATE_KEY],
      gasPrice: 8000000000, // default is 'auto' which breaks chains without the london hardfork
    }

Ref: https://github.com/nomiclabs/hardhat/issues/1828

Confirmed the solution of "The Vikk" is working. Added also the account details and 0x before the private key.

 mumbai: {
  url: "https://polygon-mumbai.g.alchemy.com/v2/<API_KEY>",
  accounts: [`0x${PRIVATE_KEY}`]
  }

I discovered the issue with "Invalid sender". This for me was that the wallet address had not sent any transactions and only had deposits from the testnet faucet. For whatever reason it made that error disappear when I sent a transaction manually through Metamask then sent it back then tried to issue the hardhat run command again.

From what I am now seeing however, the transaction still hangs without any errors and --verbose provides nothing useful. This appears to be some kind of conflict pertaining to the London Hardfork. I have not resolved the issue. Will report back later with more information if I have it.

What I have done so far:

1. Tried adding gasPrice and/or gas to the hardhat.config.js networks.matic object
2. Tried to put 0x in front of the privateKey
3. Tried adding chainId:80001 to the hardhat.config.js networks.matic object
4. Tried increasing gasPrice to over 500 gwei
5. Tried 3 different RPC endpoints including a private one requiring an API key

Hardhat github made an update to 2.6.2, which also does not resolve the problem.