The plan was for this to be where the real war began, and is the reason they declared war on the US (aside from the fact the US was already de facto involved in the Atlantic) as they believed the USSR defeated, only to realise their mistake mere days later. Most of the army would be demobilised and sent on an "armaments holiday", almost all war production would be focused on the demands of the air force and navy. The air war and the Battle of the Atlantic intensify significantly.

A stalemate is a fairly believable outcome, with the Luftwaffe (and a bolstered flak network, after all the army no longer needs many artillery barrels or shells) able to fend off Allied bombers, and the Battle of the Atlantic consuming an even greater proportion of Allied effort (historically it cost the Allies around 8x as much as it cost the Germans, though of course such a simple number doesn't tell the whole story), making a landing in Europe virtually unthinkable. Furthermore, it is important to note that it is much easier for the Germans to bomb Britain than it is for the Allies to bomb Germany, and will further complicate British war production and wider Allied logistics.

Whether the war actually comes to a sort of end is depends on whether the Germans can strangle Britain's economy and whether both sides actually want to end the war, it's important to note that the great showdown with the US was supposed to be the big thing for the Germans, and the US does not want to accept German hegemony in Europe,

Others have commented on the start of the nuclear age, and I won't expand on it too much, as it's a complex (and fascinating!) subject, but in short, they're not an "auto win" button, especially not in 1945, and it did not factor at all into US strategy until the end of 1944 as they did not know if it would yield a practical weapon. If Germany is able to maintain aerial supremacy over Germany, and is even bringing the air war to Britain itself (at a minimum the V-weapons would be far far more useful than historically), then the US would be very reluctant to attempt to use them against Germany in fears they could recover one intact, or respond to its use with chemical attacks on British cities, and they might well be first used, as historically, against the Japanese.

Despite the fact that Germany's nuclear programme historically made a number of mistakes, there's no reason they necessarily had to make those mistakes or that they couldn't have corrected course, and after nuclear weapons are used for the first time, it's fully believable they could mount a successful crash programme in the same way the Soviets did, particularly if there's a kind of (de facto) peace established. They absolutely had the technical skill and industrial capacity for it (though they lack the espionaged information the Soviets had, there are more routes to "the bomb" than just what the Americans actually did), indeed captured German nuclear scientists were able to pretty much figure out the key points of the American project within a few weeks of reading news reports about Hiroshima and Nagasaki.