Train from Wurzburg to Frankfurt for Morning Flight

Wurzburg Hbf to Frankfurt (M) Flughafen is correct. This is risky. I did something similar recently Aachen to Koln/Bonn Airport and the train was late. But I did manage to make the flight. Your train could arrive late causing you to have to rush or miss the flight.

Why do you purchase something and don't read to know how what you bought works?
This site is your new friend https://www.seat61.com/Germany-trains.htm#Railpasses_for_Germany

Your pass is valid on all DB trains, including the high-speed ICE trains. The Wurzburg Hbf to Frankfurt (M) Flughafen is an ICE train.

Maybe leave Wurzburg the night before.

What is your date of travel? I'm looking at the schedule and I see an IC train at 6:25 arriving Frankfurt airport at 7:55. You could take an earlier train which is an ICE leaving at 5:55 and getting you to the airport at 7:22. It would seem to be safe to me, I do it all the time.

Date of travel is June 16. Am I looking at it wrong? I am on this website: https://www.bahn.com/en/view/index.shtml

I am looking at Würzburg Hbf to Frankfurt(M)Flughafen

"I have purchased a German rail pass..."

A flexi-pass? Then your plans either use up all the rail pass days before the 16th (in which case, yes, you need a ticket) or you have 1 or more days remaining (in which case you just use a rail pass day on the 16th.)

A consecutive pass? Then your pass is either still valid on the 16th, or it is not (buy a ticket.)

5:55 looks right to me. I would probably travel to Frankfurt on the evening of the 15th. I don't like dealing with unnecessary variables at the last moment.

Bad luck, looks like there is some kind of track diversion going on Friday, Saturday, and Sunday, as those are the only days that train is scheduled and it is normally a 1 1/2 hour trip and it is now over 2 hours. Normal route stops at Aschaffenburg between Wuerzburg and Frankfurt Hbf, but your train stops at Hanau instead.

Given that, maybe a night in Frankfurt is in order, as there is nothing good earlier.

What are the consequences of missing your flight? An example.

I would sleep at the Frankfurt airport the night before with a 10:30 flight. Why risk it?

Don't sleep in the airport darling, (sorry Petula). Central Frankfurt is 15 minutes away on the S-Bahn.

For an international flight I would never stay so far away from the airport. It is summer, the trains are known for being delayed due to construction.

Consider staying in Frankfurt instead. The Rose and Tea light festival is at the Palmengarten that weekend. Several great Farmers Markets in the city, and lots of historic sites to see too.

For decent hotels check out Hamburger Hof, Victoria Hotel, Excelsior Hotel, the Pure, Hotel Concord, Holiday Inn Express Hauptbahnhof, Ibis on the Friedensbrucke. Do find one with AC. It has been really hot here lately.

The train takes 11 min. to get to the airport and there is a train every 15 min.

Or take an evening train from Würzburg and go all the way to Mainz. There are three hotels right across the Bahnhofplatz from the Mainz Hauptbahnhof. I've stayed at two of them, Schottenhof and Köngshof - I prefer Königshof. In the morning it's a 25 minute S-Bahn trip into FRA.