Whether a trade is a repo or a reverse repo depends entirely on which side you are. The cash lender is doing a reverse repo and earning the rate; the securities owner is doing a repo and paying it.
Money market funds do reverse repo in enormous size, both with dealers and with the Fed's overnight-reverse-repo-facility. The Fed's facility sets an effective floor on short-term rates, because no one lends below a rate available risk-free from the central bank.
Example: a money market fund lends $500,000,000 overnight at 5.30% against Treasury collateral and earns $500,000,000 x 0.0530 / 360 = $73,611 for one night.
Related: repo, overnight-reverse-repo-facility, collateral, money-market, sofr