Regex matcher with starred groups

Implement a small regex engine for a text-processing pipeline. Write is_match(s: str, pattern: str) -> bool. It returns True only when the whole string s matches pattern.

The pattern uses these rules:

• It contains only lowercase English letters, ., *, (, and ).
• A letter matches itself. . matches exactly one lowercase letter.
• x* matches zero or more copies of the single unit x just before the star.
• ( ... ) groups its contents into one unit. A * after ) repeats the whole group, so (ab)* matches "", "ab", "abab", and so on. A group without a star matches its contents once.
• Groups are never nested, and a * never appears inside a group. Every * follows a letter, a ., or a ).

Constraints: 0 <= len(s) <= 1000, 0 <= len(pattern) <= 1000, and s contains only lowercase letters.

Example 1

s = "zebeb", pattern = "(ze)*(be)*"
Output: False

(ze)* can take "ze" and (be)* can take "be", but the final "b" is only part of a group, and a starred group repeats only whole copies. No split works.

Example 2

s = "rrtuvtuvw", pattern = "r*(tuv)*w"
Output: True

r* matches "rr", (tuv)* matches "tuvtuv", and w matches "w".

Reconstructed from the reported question; details may differ from what interviewers ask.