Unfortunately, Web SQL Database has been deprecated in favour of IndexedDB, which in my opinion is no real replacement because it's a NoSQL database that's nowhere near as powerful in terms of the queries you can run with it.
However, the deprecation is understandable from a browser vendor's point of view. Maintaining and developing a browser is difficult enough as it is. Having to maintain an RDBMS adds a lot of complexity on top of that for what's probably a marginal use case for most users.
That said, it might be possible to integrate SQLite by using browser extensions. That of course depends on the users' willingness to install a browser extension in order to run your software builder.
Actually, there's a way: https://en.wikipedia.org/wiki/Web_SQL_Database (see https://caniuse.com/#search=websql for browser support)
You can see a live example with SheetJS here: https://sheetjs.com/sexql/
Unfortunately, Web SQL Database has been deprecated in favour of IndexedDB, which in my opinion is no real replacement because it's a NoSQL database that's nowhere near as powerful in terms of the queries you can run with it.
However, the deprecation is understandable from a browser vendor's point of view. Maintaining and developing a browser is difficult enough as it is. Having to maintain an RDBMS adds a lot of complexity on top of that for what's probably a marginal use case for most users.
That said, it might be possible to integrate SQLite by using browser extensions. That of course depends on the users' willingness to install a browser extension in order to run your software builder.