I’m a little rusty on all this but essentially I think the legal situation is:
There has been a long standing derogation provision in the Aircrew Regulation which allows member states to continue to apply national law to the patch of EASA pilot licensing that is covered by the LAPL. So effectively within the scope of the LAPL, national licences etc can continue to be used. This is not an exemption but a specific time limited provision in the Aircrew Reg that Member States may use. It has been extended several times since EASA Aircrew came into force and currently expires in April.
It was through this mechanism that the U.K. decided it was within its gift to allow Part-FCL licence holders to fly EASA aircraft without a medical - an EASA licence is effectively rendered valid under the ANO and therefore the licence could be thought of as having taken on the legal personality of a national one even if it still says EASA on it. So the derogation could be used by EASA licence holders without the need to get a separate national licence document. There was some internal debate at the time at CAA over whether that was a legal bridge too far, but I always thought it made sense, just about.
But the ANO also requires that the pilot of an EASA aircraft holds an EASA licence and medical, hence the need for a U.K. exemption, which was quoted in the article (although actually, now that I think about it, I’m not sure it is necessary since article 136 was specifically written in 2016 to take account of this situation, although 162 was probably still necessary). But the ANO requirement is just a U.K. legal reenforcement of EU law (not legally necessary and more a legacy thing from the way the ANO is constructed) that says you have to have an EASA licence to fly an EASA aircraft, and issuing such an exemption only has the intended effect while you have the EASA derogation provision as well, which expires in April.
Now it was getting to be almost BAU for the EASA Committee around this time of year to start thinking about what derogations should be extended for another year or two. The only awkward thing now is that the UK is no longer there to push for it. How the general EASA Comm mood is on the subject I have no idea - I have somewhat lost touch with how the other Member States feel about it. If the EASA Comm extend it in the UK’s absense, then we are OK.
The other angle is what flex we have when it comes down to it to start deviating/ignoring EASA rules before the end of year - I don’t think there is any, but believe it or not there are some creative legal minds at the CAA, so who knows...