Filtering ≠"Search"
It's amazing how often I still see people arguing about how AO3 does or doesn't have good search features while talking past each other.
I know this will be blindingly obvious to most of you, but for that remaining percentage, if you've ever thought "WTF? AO3 does not have exclude functions. What are you all on about?", you need to filter rather than search.
When most people talk about "searching AO3", they're not talking about this or this:
Yes, I know that on every other website on the planet, the default way to search is the simple search text entry box in the upper right or the advanced search. But not on AO3.
AO3 is patterned on oldschool fic archive, so the expectation is that you're looking in the index of fandoms or, in this upgraded version, starting from a ship or character or something. You're starting from a tag.
If you start from a tag, you will see a sidebar (on a computer) or have a sidebar you can unhide (on a phone):
This is what everyone else is actually talking about when they describe AO3 "search".
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Anyway, the next time you see someone claiming that Wattpad has better search features than AO3 or that exclude filters don't exist, this is probably why.
And if you're the confused person wondering why everyone else is describing the search page in a bonkers way that bears no resemblance to what you're seeing, this is definitely why.
AO3's work search is more similar to advanced search on academic journals website like ScienceDirect, Wiley, JSTOR etc. (with better capabilities at narrowing down things since the the tags are wrangled and categorized) than to wattpad.
And even in fanfiction.net people is more likely to search fics via the fandom index, then filtering fir characters, age rating, etc.
I've been thinking recently about the way the design has aged over the last 17 years. In 2008 we were conceptualising finding stuff as two complementary but different features: Search (for ANYTHING) vs Browse (cruise a specific topic). The first was for people who wanted to go as broad as possible, the second was for people who already had some sort of criteria and wanted to see what was there then narrow it down. At the time we expected people would either start with a Fandom and go straight to Browse or Search then immediately switch to Browse.
We had fandom building a folksonomy on del.ico.us out of tags for the express purpose of bookmarking content for personal and shared use. Plus to a lesser extent tagging was being used on LiveJournal. It was normal and expected to have a bunch of tags/filters to Browse! The hardest part on the AO3 was the tag wrangling feature so we could have a curated folksonomy that evolved over time.
Fast forward 17 years and for more and more people the default user experience is the mobile/app ecosystem where Search is the primary tool for finding stuff (especially if looking for your own stuff in-app, but it's the default for online shopping) followed by Browse (looking for other people's criteria-specific stuff in-app or filtering on websites after you've realised how many shoes / types of yarn there really are). In-app we Save/Download and don't necessarily consciously file things in a specific location with a specific filename, and we don't have to go back and look for things where we filed them, we can just Search. There's also a whole rant I could make about how apps are monetised and need to optimise for 'engagement' which promotes a design where Browse is as many clicks as possible which pushes users towards Search but I'll stop now.
Which is a long way to say I suspect today's default behaviour has shifted enough towards Search that Browse needs to become more visible in the AO3 user interface.