Well, SQLite has been around now for over 18 years, and is one (if not THE) most popular filebased database.
FPC/Laz supports it natively.
For Design i'd recommend DB Browser for SQLite and/or SQLiteStudio.
You'll notice that finding information on SQLite is much easier than on dBase, especially if you're struggling with an issue, you'll probably get it solved much quicker, since most of us are familiar with it.
The only thing to remember is, when shipping your program under Windows, to ship the sqlite3.dll with it (if it's not already installed on the target).
As a last advice to you (and unfortunately this applies to SQLite too!): If you're using a Database, which doesn't have a "native"-DateTime-DataType (like dBase and SQLite --> SQLite stores it as some weird String IIRC), i'd rather choose Double (If you want to store Date and Time) or Integer (if only Date), because, internally, that's what a Date/Time actually is!
DateTime --> Double --> The integer-part being the Day since BaseDay, the Fraction the Time of that day
I just did a "Debug.Print CLng(Now)" in VBA/Excel, and it returned 43559, meaning: 43559 days have passed since your BaseDay (Whatever that is)
As Double "Apr 4th 2019 - 6PM" would equal 43559.75 (The fraction being the Time-part --> at 6PM 3/4 of a day have passed)