Would that not lead to them being even worse than OTL without any lessons from RJW?
The loss was deeply humiliating for the monarchy at home and abroad, and meant that the Russians had to take on British loans in order to rebuild their fleet.
This political debt in turn meant they had to play along with the British in whatever problems they got into, meaning they would be unable to avoid WW1 regardless of German plans
or the fact that they knew their army was shit.
At home, the loss of face was one in a long line of humiliations ever since Nicholas II's coronation, and would reinforce the growing sense of disillusionment with the monarchy, which the defeat at Tannenberg would solidify. It caused great unrest and led directly to the events of 1905, and thereafter to 1917.
The main problem with Russian army of 1914 was terminal lack of supply, just as in 1853: most units had outdated equipment and were lucky if they had bullets to fill their rifles with. This came about because the army was humongous, which made reforms and installing new equipment of any kind costly, so they had a policy of keeping supplies low during peacetime. The supplies would only be increased if war looked imminent, but it was still a slow process.
The other big problem was mobilization and railroads: the vast size of Russia was underscored by the fact that railroads were always in short supply, meaning mobilization was slow and units had to move into the front piecemeal. This meant deploying into battle was slow and redeploying in case of a new front opening would be very slow.
One of the Russian army's main problems IOTL was redeploying units once it became clear that their position was no longer tenable.
With a more Europe-focused Russia, mobilization would be much quicker, supply would be easier and overall performance would soar. Combine this with much higher morale if there's no Russo-Japanese War, and the Russian army is going to look very scary indeed. While I don't agree with
@Aphrodite's categorical statement that Germany would be fucked if it focused on its army, the part about Russia is not far from the truth.
Britain, on the other hand, would not feel as threatened by Germany because they wouldn't be making moves (building up navy) which, when combined with anti-British rhetoric coming from everyone including Wilhelm himself, would turn Germany from a threat to British interests on the continent into a threat to British existence.
