I started this project a few weeks ago for my transition from Firefox to Falkon, and I've been using it ever since. It's a daemon running on a local port for all web browsers to access. It now provides two features: Top Sites, inspired by Firefox's new tab, and a search bar with customizable engines, inspired by DDG's bangs (but it's a slash instead of a bang, to save you a shift press).
Check out the source code (0BSD): [utab](https://git.sr.ht/~fkfd/utab)
utab is almost definitely *not* what you exactly wanted, given its intentionally limited config options and features, but given the power of free software anyone can build upon it themselves.