Update dependency drake to ~=1.44 (#425)

Co-authored-by: Jeremy Nimmer <[email protected]>

Author: renovate[bot]

drake_pip/requirements.txt

@@ -4,4 +4,4 @@
 # use 'drake~=x.y' instead of 'drake~=x.y.z'. See
 # https://packaging.python.org/en/latest/specifications/version-specifiers/#compatible-release
 # for more details.
-drake~=1.43
+drake~=1.44

drake_poetry/pyproject.toml

@@ -8,11 +8,11 @@ version = "0.0.0.dev0"
 description = "External examples for Drake"
 authors = [{ name = "RobotLocomotion <@>" }]
 readme = "README.md"
-requires-python = ">=3.10"
+requires-python = ">=3.10,<3.14"
 dynamic = ["dependencies"]
 
 [tool.poetry]
 package-mode = false
 
 [tool.poetry.dependencies]
-drake = "~=1.43"
+drake = "~=1.44"