There are MANY ways this can go. Regardless of the involvement of other entities, Parliament, the Church etc, the three main parties Mortimer, Percy and Glyndwr all going to want the spoils of victory. Presumably everyone understands the Welsh are not in this to continue to be under Plantagenet control surely? Any attempt to impose the Earl of March as Edmund III on the Welsh just because, when they have a viable, native alternative who has proven their will and ability to resist English rule. Any attempt to just blithely assume power like nothing had happened will inevitably be resisted by the Welsh to the utmost. He can try, but Edmund III is in some ways a default king coming after another default king (Henry IV) and will have to secure legitimacy across England and secure the North and Ireland as well.
I suspect this situation and the March-Glyndwr-Percy alliance degenerates relatively quickly due to naturally conflicting visions and goals which could be papered over during a rebellion but not during the peace afterwards. There is also the tendency of Triads to crumble after a relatively short length of time historically as petty jealousy and conflicting styles and agendas play out, often alongside the loss of life and the distinct regional differences between the different parts of England, Wales and Ireland don't really get ironed out or at least managed through thinks like standardised English, administration and railway time driven by the centralisation and regularisation that starts happening in the Industrial era.
I wouldn't count out a three-way fight between Edmund III, Percy and Glyndwr with the 2 weakest ganging up against one for mutual survival, especially if say Percy can marry his daughter Elizabeth who I think is still available to one of the two men's heir or favourite. It's not insane to imagine a war-ravaged England and these three guys fighting each other to stalemate over the spoils and then Parliament growing a pair as everyone is just sick of the carnage and decides to force the three sides into cutting a deal in 10 or 20 years. The eventual treaty probably means tolerating losing Wales to Glyndwr plus possibly some border areas say following the Teme River in Shropshire and Wye in Herefordshire as a Welsh buffer-zone, Edmund III getting southern England (Peak District south), Ireland and the claims to France which are likely still inherited by the Yorkists if he does without heirs and Hotspur and his heirs gets everything from the Humber to Berwick in the east and from around Crewe to Gretna in the west undoing the work of every English king since Aethlestan to boot.
No one really wins here: England is weakened severely, will find it more challenging to access it's holdings in Ireland and it's growth into european power in the 16th century sidetracked in its 15th century infancy whilst being saddled with a claim to France and this involvement in continental politics it can't do anything about. I would expect that English control of Calais and it's surrounding territory much more quickly, again weakening the hand of England long-term and potentially changing French and Breton politics and Flanders trade politics in ways that are difficult to quantify given the activities of the House of Valois-Burgandy in Burgandy, the kingdom that never quite was at this time. It's possible that Parliament asserts itself more in this tl, with implications for future relations with future Monarchs, but it's also possible that it breaks under the strain, especially if Burghers and Peers from Wales and the northern counties leave to form a Senedd at Caernarfon say and a Northumbrian Parliament in York. The Tudors being removed from power is a given, so no break with Rome over Anne Boleyn, no Bloody Mary, no Gloriana, so no Spanish Armada, at least not in the same way and for the same reasons and no disaster that is the Stuarts inheriting England with the dumpster fire that is British and Irish politics in the 17th century. To suggest that Oliver Cromwell remains a country squire, the Glorious Revolution and the Plantation of Ulster probably don't happen is a given, with absolutely MASSIVE consequences all around for the development of democracy, the British view of republicanism and civil war and the Troubles don't blight Northern Ireland for decades in the second half of the 20th century. I wonder though if Yorkist successors plant defeated Lancastrian supporters and other less than desirable types in Southern Ireland, say around Waterford or Wexford, the parts they can more easily access, so I wonder whether we get some form of upside down Troubles after-all - what a horrifying thought! I suspect Ireland probably generates its own Glyndwr too and goes down a similar path to Wales in this scenario eventually, perhaps the chief of the O'Neills in Tyrone or the chief of the Fitzgeralds of Kildare or someone else with much to gain or loose emerging as a new High King of Ireland.
Wales is difficult to govern due to geographical and structural reasons and needs substantial reform and nation-building to ensure a unified state able to resist Edmund's descendents and so may just disintegrate and get gobbled up by England again in time. Whatever the case the concept of Welsh nationhood is likely far more thoroughly embedded, perhaps becoming a western european, Reformed equivalent to Poland -occupied some of the time, not others, resisting it closest, more powerful neighbour all the while, undaunted.
And Northumbria has the Scots to deal with on top of establishing itself as a state and legitimising Percy authority over the entire domain, which is easier said than done, as is creating a shared identity out of what is likely to be quite a religiously diverse state going forward, possibly far more Catholic than it's neighbours for far longer and closely aligned with France, containing England to these islands which slows the development of the Royal Navy and the colonisation of North America quite a bit. Who would go? Would people go at all? Just from perspective of embedding Percy power, it's possible that Percy cuts a deal with the Beauforts, of the "recognise Northumbria and I support you to get southern England, Ireland and what's left in France" variety and we get a Wars of the Roses same but different with a younger Percy playing a decisive role as the deciding general in a rebel army under Lady Margaret's dad John, 1st Duke or uncle Edmund, 2nd Duke of Somerset...
How that affects relationships within the Isles or the Reformation is hard to say, but one can assume it will lead to the Welsh language surviving as a significant presence alone and it will absolutely pour fuel on the fire of Anglo-French disputes and Low Countries politics, just the English can't actually do anything about it...
