Good comments on fares.
One thing I could suggest is there is a national fares rise on 1 March. It is normal at the same time to alter availability and conditions of general tickets (i.e. not those special offers from TOC). It is possible the new fares tables from 01/03/23 may contain conditions changes ?
Re. access across Parkway station from the Up side (Kimpton Road) to Down side (Gypsy Lane) it would be unusual to say the least to allow cross station access. There are a very limited number of GB stations where this is possible already BUT all of them have some historic public right of way embedded into them (e.g. including but not limited to Stockport, Guildford, Sheffield) that requires access through ticket gates and use subway / foorbridge. Stockport they give you a bit of card and manually open the gates (or did pre covid not been there since) the others I'm not sure what they do.
I can't think of any station where the provision of any new facility - including any transport interchange - on one side has been provided with customer access from the opposite.
I remember there was a huge debate in rail anorak circles with the rebuilt Thameslink Blackfriars that spans the Thames with new additional entrances on the south bank. There were a lot of people getting hot under the collar demanding it as a free walking route along the platforms, that, apart from sightseeing, was based on accessing LU District line from the south bank. Unless one has reached the daily Oyster fare cap, touch in one end touch out the other does create a journey / fare / penalty.
I am not saying it can't be done. Far from it. It is very easy to implement. I'm just saying I can't think of an example where this is allowed anywhere except historic rights of ways embedded in laws/byelaws.
OK total digression but examples. Interesting to see how Luton Parkway does all this.
PS don't affect me; I have a Luton to London annual season ticket; should I wish to cross Parkway I simply enter and exit with the season.