Does any SQL engine have navigation support in CHECK clauses?
It appears you are looking for a SQL database that implements the SQL Standard CREATE ASSERTION statement. AFAIK there is no mainstream SQL database that actually supports this.

Therefore, the more complex data integrity rules that you wish to implement must be done so programmatically. This can be done using triggers in the DBMS or procedurally either using stored procedures in the database or within the external application.

However it is implemented, careful consideration needs to be made to ensure the ACID properties are followed to ensure the reliability of the database transactions. In particular this may mean explicit locking mechanisms are employed wherever the constraints are validated.

There is generally also the requirement to ensure that the constraints are enforced as efficiently as possible.

For an in-depth examination of the implementation of complex integrity constraints using DBMS triggers I would suggest reading Applied Mathematics for Database Professionals by Lex de Haan and Toon Koppelaars.