First fish of the tourney was an egg, a bit disappointed they didn't disable it or make it count toward your total during the event. As you said not a huge deal but a fair oversight

Edit: I had a single egg as the first one I caught (at 9am), I'm wondering if it was a pre-9am egg as I haven't caught another one since

Sure can! But unless you have a fair amount already stored, it's not recommended as it takes more time to farm/craft bait.

can you use fish bait during the tournament?

Tournament rules essentially has you catching as many fish in 3 minute blocks. You can play as many times as you want, and you get points based on how many you catch. Eggs do not count towards your total. Not a huge deal, but still poorly implemented.

PSA: Eggs are still in play during Tourny.