Seeing someone new but white lie?

I do think it's a red flag, but I think it's an indicator that you might not be compatible.

As PP said, your texts probably require more thought than reposting a meme or whatever, but nevertheless, it's not sitting right that he makes excuses.
The truth is he's choosing to do other things in his break OR you're not in his thoughts which isn't a great indicator so early in your relationship.

This is me, although I am long term married. I do different things at work not work related and sometimes don't text my husband as much

Nothing against him I am just in a different head space at work, not just him either

I think it sounds as though you need to do some work on yourself and getting over the aftermath of your past horrific relationships and how they cause you to react to situations before starting a new one. You’re going to drive yourself and any new partner mad with things like accusing them of lying over posting on social media when they said they were busy.

People don’t usually mean they had literally not a second to themselves when they say they were too busy to respond to a message. They usually mean “I didn’t have the headspace to do this particular task which required a bit of thought in how I answered and trying to find something clever or witty to say.”

You can absolutely be busy and then click in and out of things but just have a think about how you feel in general about him because if you’re already noticing this kind of stuff he might start thinking you’re checking up on him and you’re going to start a relationship with two people being paranoid

A Facebook addict would be a massive turn-off in of itself (it’s not 2007 anymore) but I think you’re overthinking it. It’s been a month, it’s ok to not reply straight away. This happening later into the relationship would be annoying though.

That's also fair. I mean, you know this guy five minutes. If this is already an issue, this is definitely not the relationship for you.

Well, I think you're asking the wrong question. Someone posting 'funny stuff' and football stuff on FB multiple times an hour during the working day sounds like a bit of a tool, and an under-employed one at that, so that would be what had me deciding not to progress things.

I can idly check my social media without much thought, simultaneously putting off replying to a personal message which requires more thought to put together. I imagine this man is the same, as are many people. Getting your nose out of joint because you think if he has any free time he needs to use it responding to your messages sooner is unreasonable - but if it’s very important to you that people do so, I don’t think this is the relationship for you. He hasn’t lied about anything, his time prioritisation just means he puts different tasks in a particular order.