IMO/E a 2gal unfiltered is fine to keep a Long fin male long term provided that you maintain water quality.
In 1-3gal unfiltered tanks-without live plants-water changes of twice weekly-1-50% water only and 1-90-100%- should maintain water quality-Provided that you don't overfeed and feed good quality food.
IMO/E-filters are optional for this species-especially in the smaller tanks with a Long fin male. Sometimes the water movement can cause fin damage and/or stress.
Even with a filter and established nitrogen cycle-In the under 5gal tanks-the cycle might not be stable due to limited surface area for the BB to colonize and twice weekly 50% water changes are still needed to maintain water quality, however, you can add more surface area for the BB for a more stable cycle-by way of extra sponge, bio-balls...etc....and 1-50% weekly should maintain water quality.
Live plants are also a good choice to assist with water quality and general well being of the system and Betta. However, not all live plants will do well and can become part of the water quality problem.
Look forward to seeing pics once you get it setup...