Surely the approval for approaches (RNP0.3) will also cover PRNav (RNP1.0)? I'm not 100% on that, because we don't fly any PRNav procedures, but not only does it logically make sense
You're not the only one to use the word "logical" in that context -- so does ICAO in its PBN manual. Unfortunately...
1.2.5.3 Understanding RNAV and RNP designations
1.2.5.3.1 In cases where navigation accuracy is used as part of the designation of a navigation specification, it should be noted that navigation accuracy is only one of the many performance requirements included in a navigation specification — see Example 1.
1.2.5.3.2 Because specific performance requirements are defined for each navigation specification, an aircraft approved for an RNP specification is not automatically approved for all RNAV specifications. Similarly, an aircraft approved for an RNP or RNAV specification having a stringent accuracy requirement (e.g. RNP 0.3 specification) is not automatically approved for a navigation specification having a less stringent accuracy requirement (e.g. RNP 4).
1.2.5.3.3 It may seem logical, for example, that an aircraft approved for Basic-RNP 1 be automatically approved for RNP 4; however, this is not the case. Aircraft approved to the more stringent accuracy requirements may not necessarily meet some of the functional requirements of the navigation specification having a less stringent accuracy requirement.