...The US won't be able to use San Francisco as a naval base, and the Colombia River is too shallow to support warships. That means that if the US wants a naval base on the west coast, their only real option is Puget Sound - so even more pressure on Britain to cede territory there.
Under these circumstances, I agree that the pressure is on to get as much as possible from Britain, but of course OTL borders give us quite enough of Puget Sound for naval bases--admittedly in a war with Britain against us they'd have to fight their way out of the Sound! The pressure would be on for more then, for obtaining Vancouver Island for instance, unblocking the Sound exit.
OTL it was a bit brilliant of Polk to defuse the jingoism against Britain and divert it against Mexico. Here though there is a third alternative, which is to jingo against Prussia instead. With only a few years between purchase and an American war, I'm not sure I would not side with the people in the thread who have the Americans conquering California from Prussia. Just how fast could the Prussians set up adequate shore defenses, and if they do--what stops American naval vessels from finding an alternate port, landing troops and moving overland from theire>
Say they fortify the Golden Gate. That still leaves Monterey, perhaps Drakes Bay or Tomales Bay (depending on draft), Bodega Bay and Mendocino to defend as well. After a generation of settlement, I don't doubt the Prussians could have the sea approaches neatly bracketed to all of these, and hold Humboldt Bay as well though it is not so necessary--landing there leads to nowhere! But in the short run, it may be possible to ship in enough big guns and an artillery supply to defend one major approach but trying to cover them all would leave each vulnerable. Attacking a Prussian colony is of course an act of war against Prussia, but Prussia has no power projection to speak of in America other than California itself--indeed Polk may have an extra motive, to remove Prussia from the American board before it becomes dangerous. The USA can throw whatever it takes at Prussian California to win and then settle with an indemnity paid to Prussia later. Prussia, and hence the German empire of the future if that is not butterflied, may well hold it against the Americans forever, but this will be of little consequence in America for decades to come, unless of course the Prussians are spurred into diverting effort into a massive fleet and go hunting for any foothold in the Americas they can grab in order to marshal a later revenge strike on the Yankees. But I suppose the British would have issues with that even if they sympathized with the Prussian position.
By the strongest premise we've seen in these pages for a Prussian purchase. Mexico seeks not only money but a strong ally to set up some sort of barrier against the USA, and might even be willing to compromise with Texas if this turns Texas into a neutral buffer state. Under these circumstances even if Polk sends a fleet to attack California alone, bypassing all arguments with either Britain or Mexico, are the odds high that Mexico will unilaterally attack the US to honor her pact with Prussia? Much worse for the USA is if Britain decides she prefers California staying Prussian, even without broadening an attack on the USA from all possible avenues, a simple naval engagement with our fleet would probably neutralize it. This of course is an act of war by Britain against us, but it would be most unwise, as Polk clearly understood OTL for us to get into a general donnybrook with the British empire at that time. I do believe that most of Canada other than Halifax was vulnerable to overwhelming American force if raised quickly enough. But the long term settlement will be by the RN besieging, raiding and shelling US shores, and if they like reclaiming California from our occupation if we manage to land there earlier. We might be buffaloed into accepting British challenge as a declaration of war, but it would be foolish to do so.
But this same logic means that if nothing is to be gained by war with Mexico because Texas is coopted and we don't border on Mexican territory much, it is still vital to avoid war with Britain and that means a soft voice on the Oregon question is in order. I think the USA can prevent the British from claiming any of what is OTL Washington state, but cannot dislodge the British from BC completely.
So that does leave Puget sound as a base, but compromised. If the Columbia mouth is no good for deep draft shipping, another set of compromise base sites exist--bays like Tillamook. They are not so desirable because they are not easy to access from inland, but it would be possible I think to construct railroads for essential communications, and generally rely on shipping in supples coastwise from Portland.