How can I delete sent emails older than a specified date?

That search word will not work for sent mail, because received refers to the date a message arrived. I would not try to replace it with sent.

I would do it from Sent Items instead. Open Sent Items in Outlook on the web and sort it by date, with the oldest messages first. Click the first message older than your date, hold Shift, click the last message in that range, then press Delete. Work in smaller batches if the list is long.

Deleted messages stay in Deleted Items until you empty that folder, so check there first if you delete the wrong range.

Microsoft lists the supported search words, including received, here: https://support.microsoft.com/en-us/outlook/getstarted/how-to-search-in-outlook