Erik Darling lays out an explanation of what SQL Server does to estimate the cardinality of queries using local variables. Erik covers some of the conceptual questions around how a compiler could work, and then explains what SQL Server does.
Erik talks about dependency on specific behavior and how people get upset when things change, and he’s absolutely right. My favorite example of this is the “quirky update” technique people used back in the day prior to SQL Server 2012 to calculate running totals. That technique was something that relied on unsupported, accidental but repeatable behavior around creating clustered indexes on temp tables. Even though the SQL Server team explicitly stated that this behavior could change at any time, it was clear that they didn’t go out of their way to break that functionality.