Unfortunately TfL rail services don't participate in the Delay Repay scheme. For journeys that go beyond the London PAYG area, they only pay the minimum delay compensation required under the NRCoT. This means you only get 50% of a single, or 25% of a return, and only if the delay is at least 60 minutes.
It looks like you partner was booked to be on the 18:15 from Paddington (PAD), due into Reading (RDG) at 19:06, and their onward connection was at 19:13 (18:48 ex-PAD) due into Bridgend at 20:59.
Based on the Elizabeth line train having arrived at 19:12¾, the same time the Swansea-bound train left, the connection was obviously missed. The next available service would have been the 20:13 from RDG (19:48 ex-PAD) which actually arrived at Bridgend at 22:02¼.
[The 19:18 ex-PAD runs non-stop to Bristol Parkway (BPW) and there's no opportunity to reach it from RDG using the 19:12 ex-PAD 'relief' train to BPW, as this gets overtaken by the 19:18 at RDG.]
So your partner was indeed more than 60 mins late, hence they are entitled to the above delay compensation. TfL really don't make it easy to claim this, as they say you should either post your ticket to them or call their customer services. There is no online claim form for journeys beyond the PAYG area, unfortunately.