So I bought an AT2035 mic a few months ago and just haven't been satisfied with the results. Just discovered today that it has a cardioid polar pattern and I have been singing into the wrong side. Guess it pays to read the specs.

It's not as dumb as you think. Many microphone specification sheets or owner's manual fail to tell what convention they use to identify the pattern direction. For some it's the nameplate, others the cable lock. Some you just have to test and figure out.

Back in our bluegrass band days we used a couple of AT condensers and I initially made the same mistake.

On one of mine, the 'sweet spot' is just that, a 1/8" metal dot. No other markings on the grill.

Been there, done that. Made me feel like.........

I have had to go out and re-position performers to move to the other side of the mic, so you are not alone.
Once without seeing them at the time .. it just sounded wrong on my end .. so I walked out and looked.

Had the same issue with a borrowed Behringer condenser mic that had no label. Why manufacturers don't label this, I just have no idea. Dumb for them, not for you.

A label on the mic that says 'Sing on this side' or 'You're on the wrong side of the mic'?
I don't think the performer (in my case) even considered it, as there are switches and such on the 'business' side of the mic and the other is flat.
To me it was apparent which side to sing into .. but if the singer is not paying attention, what good would the label be?
If they aren't looking for any clues to begin with they likely wouldn't notice a label.

An 'X' on the floor using tape worked here.
<grin>

No one here is this dumb!

https://www.bing.com/videos/search?q=blond+singing+on+the+wrong+end+of+a+microphone&view=detail&mid=3AB470EAD2C745461D0D3AB470EAD2C745461D0D&FORM=VIRE

But, she's ready.

Ha, I love that comic. I bring that one up a lot in conversation.

I assumed that this Behringer mic would be like any other condenser mic with pad and HP filter switch on it. Sing into the side with the switches. Nope, it was the opposite. No other singer at all, just me wondering why it sounded so wonky.

That's so the engineer can run out of the control room and flip the pad switch without distracting your singing.

A sound company tech set up my guitar microphone on stage once, and slipped a wind screen on it, since we were outside. 2 or 3 songs went by before someone hopped up on stage and turned my guitar mic around. Evidently this was the cause of so much feedback in the monitors. Not to mention nobody heard my acoustic guitar.

Had to laugh!!
This happened to me with my Rhode NT2A

For 3 days I kept quite not wanting to admit to my wife that I bought a dud !!!

It always pays to read the manual but also to listen to the mic with headphones as you explore the pattern.