I have no knowledge of PTSB, but have some from another.
Generally, banks post transactions on business dates. What I would have expected to happen with PTSB is that at some point on Friday 31 Jan, they would have rolled the business date forward to Monday 03 Feb. It seems from your experience that they don't do that until Monday.
These system were developed years ago and it's a huge business risk to implement significant change. Irish banks are traditionally risk-averse. Compliance, like SEPA, tends to be integrated around existing
systems rather than starting again from scratch.
A transfer between two accounts in your own name should not be subject to limits. If the funds allow, you should be able to move them between your own (demand) accounts without restriction.