So this will be my unfiltered thoughts on what I think this forum would need to flourish, so it's more so my vision of how SquidBoards can be the best version of itself it can possibly be even if not every goal or idea is realistic or can be fully realized at this time.
I think a native mobile app would be difficult to maintain and would create problems maintaining a consistent UI and color scheme. A Progressive Web App would likely be more suitable (supports more than just mobile devices), make development easier and require significantly less storage space.
Given the Splatoon 2 decor, I don't need to mention that the look is outdated. However, I think basing it around Splatoon 3 isn't the solution to it either. My idea here would be to create a more 'timeless' design that has a general over encompassing inspiration from the series itself. This would also give the forum a more unique look and provide opportunities for artists in the community if any wanted to participate. This is still a forum however so there's no reason to can the old design, many forums let you choose from a variety of themes. It would just generally be best for the 'timeless' one to be the default and signature look.
Restructuring the forum categories or including new ones for Salmon Run, Tableturf, etc. would also be very valuable to the subcommunities of the game and prevent discussion from getting lost in a general Splatoon 3 subforum. Additionally, I am aware that some Splatoon fans may not even play the game itself and are immersed with the lore, design and art of the game so it would be beneficial to members and moderators to update and clearly define what each subcategory is for. In the event that SquidBoards is able to gain some serious traction again, I think it would be good to open 'General' subforums for fans of the game that do not speak English. This would primarily serve to be as welcoming to the overall community of the game as possible but an idea that would definitely need more fleshing out if it were to take form.
Integration with other Splatoon dedicated websites like Inkipedia, sendou.ink, etc. would also further encourage people to use all these services together and give people less of a need to rely on Twitter or being in the "right" Discord server to be able to reliably find information and discussion on a certain topic.
I will admit that I haven't really kept up with the well known names since the Splatoon 1/early Splatoon 2 days so I can't give concrete people for this one but going back to the idea of subforums. I think it would be beneficial to have moderators who are most familiar with that subforum's topic to be in charge of keeping discussion in the right direction and could relieve "General" moderators from having to keep discussion from going off-topic. GBAtemp.net is the only forum I'm aware of that has a structure like this.
Lastly, this last one is definitely more of a hope than a suggestion of mine but having a more centralized hub could provide a safer and healthier place for younger Splatoon players to be in. I know it's not going to prevent bad things from happening but it can combat malicious and predatory behavior by not having as many things go under the radar like they would on a general social media site. It would also expose them to more nuanced takes and further develop critical thinking skills just by lurking here and seeing veteran players fully lay out their thoughts on here. It's a fine line to walk too since you don't want over-moderate and deter people from wanting to stay here but keeping ****-posts and spam to minimum is important.
tl;dr - It will be a massive community effort and will need serious commitment from everyone to make this last and not be a short-lasting bubble.