Receiving an offer after accepting another offer.

If the offer from company B is substantially better, you should take it. Your employment in the US is at-will, so there's absolutely nothing illegal about reneging. (You'd likely have to give back any signing bonus)

However, you're right you may potentially burn bridges. Two things to note:

1. I'd feel less bad about it if you're a mid-level dev at a large company. e.g. if you're L4 at Meta or Google, take solace in the fact that you're just not that special. So, you leaving is not too disruptive to the company.
2. You should always phrase why you're leaving a company as "I got a compelling opportunity elsewhere, but I still loved working with the people here and the mission you're all working toward."

#2, I've never seen that happen. Once you've signed the offer and joined a company, you lose almost all your leverage.

What is the best way for me to renege the previous offer without burning bridges?

There is none. Companies (understandably) hate reneging. Giving an interview + extending an offer takes a ton of human resources (more than you spent going through the loop), so it really hurts when you re-neg.

Did anyone here show a competing offer to Company A (after signing) and try to re-negotiate or move the needle? Has it worked for you, if you did this in a polite manner?

As Rahul mentioned, this won't work. You have already signed.

Congrats on the offer! If you're able to secure more offers, here's our negotiation playlist: [Taro Top 10] Pay Negotiation