I think they finally dredged the inlet. Until then many deeper draft vessels, including commercial fishing vessels, were restricted in their use of the inlet.
Montauk is a place of contrasts. The harbor is a fishing Mecca with well heeled fishing machines and I suppose you could say "The gold chain" crowd. And, there are day boats on which less well heeled folks will find a place. In the Harbor area there are modest eateries such as Salvators where there was a mounted head of Frank Mundus's record Great White Shark and pool tables. Then there are formerly modest eateries which have upscaled for the NYC tourist crowd - which are now expensive. There is the whole Gosman's complex which could be regarded as a tourist trap, but serves up a high quality lobster dinner which you can enjoy while watching marine traffic transiting the inlet. If you have access to a car there are many other eateries including Durea's - which is very expensive but has a great Sunset view and if you are into it you may see some celebrities, Gurney's Star Island Marina/Yacht Club where I purchased the most expensive lobster yet at that time in my life. There are other dining options in town and going west towards East Hampton including the famous "Lunch."
Outside of the Harbor area, there is ocean beach access, Montauk Downs Golf Course (Public), Camp Hero - where the US Government was experimenting with large radar, Montauk Point State Park, numerous hiking trails, a Dude Ranch where you can ride horses or even see an occasional rodeo.
Montauk is a very special place, where I spent my honeymoon night and many anniversaries since. It is a geographical jewell jutting out into the Atlantic and with it's micro-climates (Fog).
It was undergoing a metamorphosis when I left NY and I can"t say how covid changed it.
I never went by boat. It was regarded as sailboat unfriendly by locals on the North Fork. While I know folks who have anchored in the lake I never did because I always figured that would be the time the lake would close for transient anchoring. The next real harbor is Three Mile which is a bit of a slog.