I'm rusty on my canadian history, especially on immigration patterns, but Britain does need to populate the area. One of the causes of the AR was an attempt to limit white population. Long term, that is not viable. There's various leftover French settlement (Illinois, Indiana, Detroit) which is going to grow. Folks will move in, especially from USA, and the question becomes whether Britain/Canada turns a blind eye (long term untenable for native relations/policy) or actively enforces the ban. It's really too inviting a region for white settlement for it to remain a native reserve.
Growth/development of the region depends on whether Britain decides to grow Canada or simply let it slowly develop itself and grow mainly through natural population growth.
Militarily, the region is going to be a target during any future conflict with USA. After the AR, 1812 is not foreseen, nor is it guaranteed to happen, but Britain has to recognize that conflict is a potential, and that Ohio/Indiana/Illinois would be an easy target with some sort of military enforcement. Then again, this ATL USA is coming out of the AR a little worse for the wear, so war may be butterflied completely out of the picture.
Ohio is a target for early development. It's sparsely populated by natives and is good farmland. Eastern parts have mineral resources, and it would act as a buffer against US encroachment.
The southern St Laurence river valley is likewise a target for early settlement.
Where Britain gets the people to settle is a good question. Natural population growth is strong, but the starting numbers are so low that it's going to take a while to get going. Britain is still going to provide a steady flow, but USA, land of the free, is going to be a big competitor for attraction of immigrants. Or ATL USA, being more beat up, may implode/balkanize/otherwise end up a mess.
Access to this region is going to be the St Laurence/Great lakes. Need to develop the canal system for water travel/shipping. Access also up the Mississippi, which means Steamships. that age is still 2 or 3 decades away from end of AR. This also impacts relations with Spain/New Orleans. Britain will want to have access on the Mississippi, and has the military might to enforce it. Spain will bow to British pressure. They did OTL when Britain backed USA, and they will here.
Louisiana Purchase. An interesting dilemma. Diminished USA may not have the enthusiasm, might, or money to want it, to demand New Orleans, or afford it. Britain is going to be an active party with interest in what is going on with the port and the river, no matter how active they are in developing the Ohio region. The notion of the sale may be butterflied away. During the phase of war between Britain/Spain, and then during the French ownership of it, Britain may decide to take it by force, and now you have a new territory added to the Ohio region. Britain/Canada may not want it, but they also have to recognize that control of the Mississippi Valley is important for Ohio/Canada, and depending on relations with the US, may not want the US to have it.