I use Outlook Web Access at work and have set up rules for filtering emails by client email domains into different folders.
Is there a way for me to apply these new rules to messages already in my inbox?
Although the Outlook desktop client allows you to run rules against a mailbox (including inbox), not all features work the same in Outlook for Web Access (OWA). Rules is one of them.
As you can see from the screenshot below, the wording says, "When the messages arrives, and". This means your rules only apply to new messages. Existing messages, like those in your inbox, do not qualify for processing. You have to move them manually to each respective folder.
Even though this feature is unavailable I found a way to not get bogged down too much doing it manually.
(If you try to scroll all the way to the bottom, the shift-click won't work, at least as of now.)
There is a limit (250 threads) to the number of search results you will be shown, so if you exceed that limit you will have to repeat even this procedure several times until your Inbox is clear. However, do not repeat your search immediately. Do something else for a couple of minutes and then come back and do it. Because the emails will be moved/processed in the background, and until that completes, the same search results will be returned, and you will repeat your work. There is nothing in the UI to tell you that this is happening, but when the work completes, the search results will be different.
While Microsoft could just implement the "run rules against inbox" feature that other online email clients have, this procedure is still way better than moving them one at a time or 8 at a time using the "select all (at the top)" button.