I mean sure, if you ignore the fact the German Naval buildup was specifically design to challenge the RN and had passed several naval laws to such purpose, the freakout about german fleet was nothing to do with its growing size...
It was built to challenge it eventually, but was incapable of doing so. Pre-war, the British Admiralty was very well aware that this was the case.
It is impossible to explore alternate outcomes to the Anglo-German naval race without taking into consideration the role of internal politics on both sides, and for the British this means the invasion war scare and all the related scandals. I would recommend reading Andreas Rose's work Between Empire and Continent - British Foreign Policy before the World War for more detailed explanations on how the invasion scare was used as a lever for domestic political success, and securing funds, by many actors, even while the Admiralty reiterated time and again that the HSF was incapable of threatening the British coasts. Press Germanophones like Repington and Maxse were instrumental to the desire of the Liberal Imperialists to 1) leave splendid isolation by joining the alliance system on what they thought was the stronger side, i.e. France/Russia, and 2) avoid what happened to the radicals in the khaki elections: lowering the defense budget, and paying the price with voters.
To be clear, Britain was just as useful to German domestic political circles as a scapegoat and an excuse to push forward partisan political projects. I'm only focusing on Britain because it is the one point where the old narrative of German action and British reaction still holds sway, even though any archival search for the British side clearly reveals that the calculations taking place were quite different, and that Britain was proactive, not reactive - as it befits the greatest naval power of the time. Even Repington admitted that his press campaigns against the Reich weren't motivated by the existence of the HSF, saying that the Channel Fleet "is by itself a match for the German fleet, and reinforced by the Atlantic Fleet, it has an overwhelming superiority in the world. ... The truth is ... our superiority over Germany is so overwhelming and the superiority of our personnel and of our gunnery practice is so great, that the Germans know it would be madness for them to provoke war."
I want to thank @Erzherzog_Karl who first made me aware of the literature in this regard and who's far more knowledgeable on the subject than I am. But I also want to close on a final note. Many works of alternate history that focus on Germany - and this timeline is not one of them, one of the reasons why it's one of my favourite works on this site - tend to fall into a misleading pattern where Germany is "the player" and everyone else is "the game world". Germany takes an action, the rest of the world reacts. If Germany chooses different, then the rest of the world also chooses different.
But the real world is more complex than that, butterflies notwithstanding. Other countries have agency. They have their own foreign and domestic problems, and political plans that exist independently of what Germany does. Germany by itself isn't going to chase away the political pressures placed upon British parties by the khaki election, to go with the relevant example. In this TL's postwar, just like in an alternate prewar scenario, Germany might even decide to go with what they think is the best way to ensure peaceful coexistence with Britain, but that doesn't mean they will magically get it, because Britain has its own problems and its own plans.