So my Sim started the work day with "Socialize with Co-Workers" then a few hours in I decided to switch to work hard, but I noticed that I was still gaining relations with my Co-Workers, is this normal, or is the meter bugged?

I think it just takes a while to update.

Actually, it's normal. Sims gain social relationships with coworkers even when on Work Hard, Business as Usual, or even Slack Off, just at a slower rate than with Socialize.

I just noticed my Sim gaining friendships while working from home, is that normal too?

What's likely happening is that your co-workers are using the socialize option. You'll have a relationship gain even though you're working hard because co-workers are socializing with everyone, including your Sim. I like to check to see what the others are doing while my Sims are at work.

Are you using NRaas Story Progression, btw? Because that one can push stuff like that onto inactive sims.

Oh, wow! I didn't even know this was possible. I never paid attention to this.

Not sure if it actually does it for all professions, but there are some where you need to be friends with the coworkers to promote. And I'm pretty sure that SP makes sims work towards their promotions, so...

I do use story progression, so that's probably it then.

I just tested it out with my workaholic surgeon. When she works at home, her fun maxes out, but her social will slowly decay if she doesn't take a break to do some social thing like talk to someone. Is that what you're talking about?

Now, I wasn't looking at her work relationship values with coworkers for that mini test, but as she's already best buds with everyone, I wouldn't see a positive change anyway.

So working at the office, all tones will fulfill social, and gain you friends with coworkers, albeit at different rates depending on Work Hard, Business as Usual, Slack Off, or Chat at the Water Cooler. Working at home, in my game at least, does not raise the sim's social. I am using Twallan's SP as my default as well, and don't recall changing any options relating to careers and befriending coworkers, if such options even exist. Not really sure what to tell you at this point.

Only actively interacting with coworkers should gain you relationship points with them in an unmodded game. The other worktones can raise the social need but the relationship status should remain unchanged.
I know of one one example where relationship values rise without interacting with the Sims anymore, and that is after having played tag with the Sim(s), which can cause the tag players to become stuck in a PlayTagSituation. So, in a way they're still playing virtual tag.
But maybe there are other situations that can become stuck and have that effect. Wouldn't surprise me. Checking a Sim's personal status in MasterController often reveals whether they are in an ongoing situation scenario.

I didn't notice if she was gaining any social, I was just notified that she became friends with a coworker while working from home.