Being assertive IS important in your career. Your colleagues are the unprofessional ones here. I would not tolerate someone sending me “lol” in a professional context and would quickly correct that behaviour.

A factual reply is all thats needed “you asked for a solution, this is the solution. Please do not be dismissive or rude. If you want an alternative please look for yourself, just expect the cost to be significantly higher. Otherwise I’m happy to discuss any concerns which are easily addressed such as branding”.

There is a huge difference between being rude and beibg assertive. They’re clearly being rude. You need to be assertive in response.