> but searching for it isn't that much of a bottleneck?
If you look up from your text editor even a second, it will take several seconds to get back into context. So even if the page you want is already in your browser, and you just switch windows, you lose.
Also autocomplete has three purposes: prevents unnecessary typos, is faster than writing it out, and lets you find API/docs.
How long it takes to find a relevant piece of code in your code base obviously depends on what tools you have for searching your local code, how much code it is and how good the search is. How long it takes you to find something online depends on how good the docs are etc.
How much value autocomplete is also depends on the strength of the type system of course. For C or Javascript there isn't much autocomplete can do with the contextual information, but with Java there is a ton to be gained (Long method names are norm, and object-dot notation feels almost invented for autocomplete). So if I were using something with a functional flavor, or a weak or dynamic type system I'd probably have a different opinion. But for strongly typed OO (C++, Java, C#, ...) the value for autocomplete is enormous to me.
Without autocomplete you can always make longer descriptive type/variable names because the time taken to write a type name isn't proportional to the length, only to the unique prefix or unique camelcase signature of the type name. E.g. for a DefaultUIRenderer I could write DUIR-Tab and know I had the right type (Insert obligatory Java joke about ContextFactoryProviderFactoryDecoratorVisitor here). How much you gain on this depends on how good a typist you are obviously. I have an error rate of around 1/10 chars being backspace, and you might argue it's because I do auto complete, I don't know...
> There are auto-completion tools for text editors, but I just never invest the time to activate or configure them
Me neither. That's why I think any reasonable IDE should be either a) working out of the box. I.e. hope that you can find an editor/IDE that ships with batteries included, or b) that it's at most a matter of selecting one plugin from a menu to activate support for language X in the editor. If I have to start configuring something with a text file somewhere then someone failed, either the makers of the language or the editor or both. Even in "plain" editors like VS code or Sublime you can usually just get a plugin these days.
> AFAIK there aren't completion tools which work well across different languages.
There are efforts to do this, but the name escapes me - that is, an effort to remove N languages times M editors and make a standard for syntax highlighting, autocomplete etc. that makes at an M+N problem instead.