How is the prioritization of Bitcoin Transactions done as of today?
The (close-to¹) highest block reward is achieved by including the transactions with the highest fee per weight. Deviating from that, miners are free to include any valid transactions at whim. They may for example choose to include their own transactions, transactions for their business partners, or transactions subsidized by out-of-band payments over other that would gain them higher revenue.

While a miner could still choose to select by coin-age-priority, this would neither be economically rational, nor supported by default by the latest versions of Bitcoin Core. Coin-age-priority was deprecated in Bitcoin Core 0.12.0.



¹ It's fathomable that a case could be constructed where selecting strictly the transactions with the highest fee rate would leave the block not completely full and selecting other transactions instead would increase the absolute revenue.