Store search query and filter options state in URL params

[shintyl]

The changes in this PR persist the current search query and filter options of the Welcome page in the URL params, which allows users to link to a version of the Welcome page with a specific pre-populated search query and/or filter options. This is mainly designed to accommodate users that bookmark/pin a tab for downforacross.com and are only interested in viewing New puzzles that fit a certain search string, and don't want to look through the full list of puzzles or enter a search string when they open/refresh the page.

Demo

https://user-images.githubusercontent.com/14168765/231033457-31af2697-69ea-4021-9387-f011895c302e.mp4

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Name	Status	Preview	Comments	Updated (UTC)
downforacross.com	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Apr 11, 2023 2:18am

[stevenhao]

nice feature idea, and a pretty clean code diff too. thanks for contributing!