Why doesn't verified proxy contract show underlying functions on Etherscan?

I have deployed an ERC1967 proxy contract and had it pointed to a UUPS implementation contract. I have also gotten both contracts verified on Etherscan.

Both contracts are verified successfully on Etherscan and I can see the green checkmark on the 2 contracts. The codes are also showing up on Etherscan under the "Contract" tab.
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For the implementation contract, when I click into the Read/Write Contract tab on Etherscan, I could see the list of functions.

For the proxy contract, however, when I click into the Read/Write Contract tab on Etherscan, it says Sorry, there are no available Contract ABI methods to read. Unable to read contract info. for read and Sorry, no public Write functions were found for this contract. for write.

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I have seen other proxy contracts and they usually are able to see the functions in the underlying implementation contract on Etherscan and 2 additional tabs "Read/Write as Proxy". But not in my case. Why doesn't my proxy contract show its underlying functions too? Did I do something wrong with my contract or verification? I have tried it on Etherscan and Polygonscan, and the same issue happened.

On your proxy's Contract tab (as in your screenshot), on the right side, click "More Options" -> "Is this a proxy?", then click Verify with that proxy's address.

This will cause the "Read/Write as Proxy" tabs to appear.