The Russo-French fleet was far from a "non entity" and French designs were good. The problem with the Borodinos were the redesign that left them top heavy.
The problem with the Borodinos was that they were a (poor) copy of the French built Tsesarevich which "
Like the French ships, though, she was top-heavy and lacking in stability, and had longitudinal watertight bulkheads which made her prone to capsize if holed on either side." Being top heavy was a French design feature.
English ships also had lots of technical problems (Fisher would scrap over half the fleet as obsolete and worthless)
Obsolescence is scarcely a technical problem - surviving until old age is seen as virtue in many cultures...
Russia's power in the Far East was already immense- second only to Japan's and growing very rapidly. Once the Borodinos and the railroad was finished, Japan's position would be well nigh impossible. Russia's failure is in not closing that gap three years earlier
Russia made mistakes in its far east policy- not dealing Japan the death blow in 1895 when she could have forced Japan to give up all her gains, seizing Port Arthur and thereby losing the Chinese alliance and pressing the Manchurian issue a year too soon. Given the balance in 1904, cutting a deal with Japan would have been the safest play.
Aside from Russia's growing power the logic of cutting a deal, I disagree with everything else outlined above.
But all that said, a scenario where Russia defeats the Japanese and destroys her fleet in battle is quite plausible and the ramifications of that is what I was hoping to explore
Here goes:
- Russia re-establishes itself as the English nemesis, resulting ultimately in reconciliation between Germany and England. Entente membership is subsequently limited to France, Russia and Serbia...
- Russia continues to spend vast sums of money on the Trans-Siberian railway in addition to its now enhanced navy. With the 'true worth' of the Russian navy demonstrated, perhaps a fourth fourth fleet on the Murman Coast is a possibility. To remain competitive, 50% of the Russian defence budget would need to be spent on its navy.
- OTL the Russians often relied on Chinese managers to maintain their limited Manchurian holdings - expanding those holdings would be expensive and difficult. Further, from 1895 China was successfully encouraging massive Chinese emigration into Manchuria to thwart foreign influence/ control.
- If Russians seeks to expand control into Korea, management difficulties become more difficult by high population density. Any civil unrest among those now ethnic minorities would be subsequently encouraged by Japan, China, USA and England - if their initial demands of for Korean sovereignty were ignored.
- With the Japanese navy defeated, it is likely augmented sufficiently by England or the USA to ensure safety of the Japanese homeland. Some parallels to post WW2 Korea/Japan, without the imperialist baggage - a potential Japan wank

.
- With an under-resourced Russian army and German-English understanding, terms like German Morroco and/or German Indochina might be in everyday use - a potential German wank

.
- In summary, Russia will have fewer friends, a more fragile economy and an army that overdue for a world of hurt.