"range query" is different from "find next availability".

Do consider to explicitly use 16(-ish) bit pointers instead of native sized ones, and go for a SIMD-friendly binary trie; with some degree of implicitnes where it is addressed as if it was storing a set of mutually prefix-free variable-length (capped to something though, like 32 in your example) bitstrings (no entry is a prefix of another entry), but you're not looking to distinguish `{00, 01}` from `{0}`.

Operations are restricted, but it should be able to be very fast for "find first empty of at least X large starting at or after Y" as well as "clear from X to Y inclusive" and "add/mark from X to Y inclusive".