Pretty much all big flights searching sites (flights.google.com, Bing, etc) allow to specify that you have luggage, and the search results changes (sometimes quite drastically) depending on that checkmark.
I'd note that some airlines don't show up on the aggregators (like Southwest).
By luggage on Google Flights you just mean carry-on, right? I've never seen a Checked Baggage option
Google Flights lets you select the number of bags and updates the displayed flight according
(Anecdote from recent domestic US travels, your mileage may vary, etc etc)
And Google Flights shows extra notices that this or that is not allowed or included - for each specific flight.
Carry on bags, right? Not checked bags
The problem is that airlines have a financial interest in hiding that info from aggregators.