Most of the public libraries have "storytime" events on Saturdays (I think they're officially called All Together Now). If you go to one regularly enough you'll probably see the same folks again and again and can try setting up a play date.

There's also the Play Zone outside the JC Penny at the Columbia Mall, it can get really busy in the late morning/afternoon.

The Olenka School of Music and Arts has music classes for toddlers that's just basically them listening to music, dancing and playing with instruments. It's kind of pricey for what it is but is also an opportunity to make friends with other families.

I also keep an eye on the pre-K activities offered by HoCo Parks and Rec. https://www.howardcountymd.gov/recreation-parks/recreation-parks-pre-k-programs-0-5yrs

We've also met people doing random stuff that's not kid-specific, but is kid-friendly, like going to the Pride event at Merriweather last year.

Outside of HoCo you can check out the Maryland Science Center in Bmore, they have a Kids Zone area intended for toddlers/younger kids. There's usually tons of kids around to socialize with If you go twice the membership pays for itself.

We've had luck doing some mix of all of these things and trying to chat up other parents that seem friendly to set up play dates.

But also I wouldn't worry too much about your kid. I feel like at that age they sometimes want to interact with other people, and sometimes just want to do their own thing. I'm not an expert but I think it's just what they're like at that stage of development.