Can I use get_adjacent_post for specific categories?

What you call “slugs” here is more appropriately called terms. It is a little confusing with native taxonomies because it turns into tautology: individual categories are terms of the category taxonomy.

So sports and tech are terms of native category taxonomy.

The function arguments operate on taxonomy level, not term level. That is you need to provide a taxonomy slug, such as category, and all of the terms in that taxonomy will be considered for a match.

From arguments point of view one of the options here is to use $excluded_terms argument to exclude everything but the one term you want.

Other than that it’s pretty low level function, which directly generates a lot of custom SQL. There are abundant filters for manipulating that part of the process, like get_{$adjacent}_post_join and get_{$adjacent}_post_where, but it’s not something I would call easily adjustable.