update next-typecheck and table (#38567)

doc/analyze_check_versions.md

@@ -6,7 +6,7 @@ This table is to clarify the currently pinned version of tools we run in CI and
 | Tool | Current Version | Next Version | Next Version Merge Date |
 |------|-----------------|--------------|-------------------------|
 Pylint | 3.2.5 | 3.2.7 | 2025-01-13 |
-MyPy | 1.10.1 | TBD | 2025-01-13 |
-Pyright | 1.1.371 | TBD | 2025-01-13 |
+MyPy | 1.10.1 | 1.13.0 | 2025-01-13 |
+Pyright | 1.1.371 | 1.1.389 | 2025-01-13 |
 Sphinx | 7.3.7 | N/A | N/A |
 Black | 24.4.0 | N/A | N/A |

eng/tox/tox.ini

@@ -170,7 +170,7 @@ commands =
 
 [testenv:next-mypy]
 description=Typechecks a package with the latest version of mypy
-mypy_version=1.10.1
+mypy_version=1.13.0
 skipsdist = true
 skip_install = true
 usedevelop = true
@@ -219,7 +219,7 @@ commands =
 
 [testenv:next-pyright]
 description=Typechecks a package with the latest version of static type-checker pyright
-pyright_version=1.1.371
+pyright_version=1.1.389
 skipsdist = true
 skip_install = true
 usedevelop = true