Is this viable grounds for appeal?
No, code 01 has nothing to do with yellow lines, it's to do with waiting prohibitions (which for instance require no lines in a restricted parking zone), yellow lines just happen to be the most common way of indicating a waiting restriction.
Waiting restrictions generally extend across verges and footpaths up to the boundary of the highway, it is a common misconception that you can get round a double yellow line restriction by parking on the "
other side" but that is just a misconception (otherwise everyone could park wherever they want by just parking on the pavement rather than the carriageway).
As for your second point, this wording on the back of the PCN plainly covers the requirements:

The PCN does not need to quote the regulations verbatim, it just has to get the substantive message across, which this wording does probably better than any other example we've seen.
Here are the council photos:
DR1495737A:




DR14957369:




As we know from the Court of Appeal judgment in
Dawood, R (on the application of) v The Parking Adjudicator & Anor [2009] EWCA Civ 1411 as further clarified by the High Court in
Pereira, R (On the Application Of) v Environment And Traffic Adjudicators [2020] EWHC 811 (Admin), who owns the land under the highway is irrelevant (the land under almost all highways in the country is privately owned, including in all likelihood the road outside your house).
So, there are three issues here:
1) Is there a traffic regulation order to support the restrictions?
2) Were the cars parked on the highway at all? We would normally say that the road extends as far as one can go without getting to a physical boundary such as a wall, fence or so on. Obviously this can only go so far because if the carriageway were adjacent to an open field with no physical separation such as a ditch, it would be a nonsense to say the whole field is part of the highway, but it then becomes a question of fact and degree.
2) Is there a legitimate expectation that you could park there?
To get a definitive answer on point 1 I will have to ask the council, it can take 20 working days to get a reply (possibly longer, sometimes quicker).
As for point two, I think if the cars had been parked where the red car is seen here
https://maps.app.goo.gl/2vbhyFpfLz5WoDLs8 they would have likely been safe as that is far too far from the carriageway to be objectively part of the highway in any meaningful sense, but as the cars were right next to the pavement I think this argument is a non-starter.
As for point three, there are 12 Google street view captures between 2008 and 2023 and of those only three show cars parked on the grass, so there is no prima-facie evidence of any legitimate expectation. If you wanted to pursue this angle, you'd need to provide witness statements, I'd suggest one from the cathedral would hold a lot of weight.
The statement would need to spell out exactly how many people park their cars there, when and how often this happens, how long this has been going on for, and on how many occasions penalty charges have been served on cars parked there. The best way to get an evidentially watertight statement would be if I could have a chat with whoever from the cathedral you are in contact with and then I could draft some wording and you could give it to them to sign. Please contact me via PM if you'd like to arrange this.