Bump pydantic and fastapi to support Python 3.14

[tw4l]

Fixes #2947

Bumps pydantic and fastapi to latest versions, pinned to specific versions to ensure we're not accidentally affected by a breaking change.

Nightly test run from this branch: https://github.com/webrecorder/browsertrix/actions/runs/20763173552

[socket-security]

Review the following changes in direct dependencies. Learn more about Socket for GitHub.

Diff	Package	Supply Chain Security	Vulnerability	Quality	Maintenance	License
	glob@​8.1.0
	sinon@​12.0.1
	replaywebpage@​2.2.4
	postinstall-postinstall@​2.1.0
	regex-colorize@​0.0.3
	update-dotenv@​1.1.1
	lit-shared-state@​0.2.1
	url-pattern@​1.0.3
	rollup-plugin-typescript-paths@​1.4.0
	tlds@​1.259.0
	ink-mde@​0.33.0
	postcss-lit@​1.1.1
	yaml@​2.2.1
	husky@​8.0.3
	parse-ms@​4.0.0
	micromark-extension-gfm-strikethrough@​2.0.0
	nanoid@​5.1.5
	webpack-merge@​5.8.0
	pretty-ms@​7.0.1
	micromark@​4.0.0
	fuse.js@​6.6.2
	iso-639-1@​2.1.15
	slugify@​1.6.6
	patch-package@​8.0.0
	http-proxy-middleware@​2.0.7
	webpack-cli@​5.1.4
	thread-loader@​4.0.4
	html-loader@​3.1.2
	style-loader@​3.3.2
	lodash@​4.17.21
	storybook@​8.6.12
	remark-gfm@​4.0.1
	query-string@​8.1.0
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[tw4l]

@ikreymer No rush but this has been tested locally and appears to be working well without side effects