Seems like what you should be asking for is Mastodon, but with performance improvements and improved search.
Or the global community of people with some technical proficiency keeps developing Mastodon (or forks, or OSS replacements) so that it is a real replacement.
My stance on future Twitter-like proprietary social networks is clear and unequivocal: Never again.
It’s ran for over a decade, not a bad run. I’d very much be surprised if Mastodon instances last that long.
Decentralisation brings its own major issues, it’s not a silver bullet. Thinking that Mastodon-like services will take over is a pipe dream.
Proprietary services aren’t inherently bad as long as their business model aligns with your interests. The problem is that the current business model of social media is “growth & engagement”, not actual money from end-users. This means the relationship between the provider and the user is always adversarial and there’s an incentive to pull tricks like this so you steer users back into the malicious, official client to collect more data and/or harass them with dark patterns.
It is absolutely possible to build and operate a sustainable social media platform by charging a monthly token sum for the service. The only reason it’s not done nowadays is because there is no room for new players to enter - without interoperability either enforced by law (EU digital markets law?) or adversarial interoperability being made legal (the law is currently abused to prevent that), a new general-purpose social platform is a non-starter regardless of the underlying business model.
How many zero sum whinging headlines have we had to endure in that time? Twitter bans Joe Blow. Twitter bans third party app. Twitter has too many bots. Twitter doesn't have enough bots. Twitter censors subject blah blah. Twitter drowned a puppy (allegedly). Twitter finally bothered to release feature X. Twitter demands phone numbers for better surveillance. Twitter makes new release that totally fucks over the way you use it. Twitter stops software from working on older devices. Twitter doesn't support this desirable usage pattern. And so on ad infinitum.
The breath of fresh air, which is actually just how things were before the web 2.0 catastrophe, is that libre software and libre services escape that centralized crab bucket. If you want a feature go ahead and build it, or donate to those who did/will. Or just wait, because rather than being a tug of war over what one client does, many different ones can bloom.
If you want the features a centralized service can bring, use a large server that implements them, which will shake out over time. And if it turns out they just develop the same monetization pathologies that Twitter had, you can easily move on without changing everything. The less costs to switching there are, the easier it is to go your own way. That's the benefit of an open protocol.
Twitter was an idea? The original "stat.us" idea was something like "Social SMS, to broadcast to your friends what you're up to as you go about your day." Jack Dorsey admitted that they had zero clue that Twitter would arrive where it has.
What is needed is to do Twitter again, in some way that is more open and supportive of client apps, but still has the immediacy and global search that Twitter has. Mastodon has its uses, but it isn't a real replacement. Twitter was always a terrible business, but an incredibly useful idea. The idea needs to exist.