Sounds pretty unreasonable to me.
Barring him from an entire lesson because he’s 5 mins late in the first week of a one-way system is hardly going to help his education. Then, looks like the 1:30hr one is a Head of Year. Followed by isolation of 6hrs. Then suspension. No need to escalate it so far without speaking to you. It’s non a blooming overdue parking fine.
This happened to my DC once or twice, who told me there were more kids in isolation than in some classes. One failed occasionally, at your DS’s age, to attend detentions, but politely argued their case and were let off. Or at least told to sit it the next day.
I’d complain via the school’s complaints procedure, which should be on their website. Set out reasonable arguments, as you have here, for the suspension to be lifted. If he’s been struggling to attend, they should be encouraging rather than excluding him, unless his behaviour is unacceptable in some other way (rude, non-compliant, disruptive etc). If he’s polite and well-behaved, a suspension is bonkers IMHO.
It’s important you’re very respectful about the need for their policies, e.g. if kids trail in more than 5 mins late to classes it disrupts the start of the class, eating into precious teaching time. It’s important he acknowledges this and shows he understands why they need this rule. And commits to allow enough time to be punctual in future. You may have to compromise, e.g. by him agreeing to the 6hr isolation. I’m sure they’ll let him have screen breaks to prevent a migraine, if he takes a book. And 15yo are generally used to looking at screens for hours.
Good luck.