According to S.C.M Paine's "The Japanese Empire: Grand Strategy from the Meiji Restoration to the Pacific War" the Japanese massively over-extended themselves by the time of the Treaty of Portsmouth. Japan had struggled to fill the ranks for the decisive Battle of Shenyang and although they won their army was exhausted from the fighting. Russia had had a decisive military advantage in terms of manpower during the war but had failed to utilise it and had made unneeded and costly blunders such as the deployment of the Baltic fleet.

An example of just how close the victory could be would be in the Siege of Port Arthur. Roman Kondratenko, the Russian general defending the port, stubbornly would not surrender the fort despite very high casualties from both sides ( 57,780 for the Japanese, 31,306 for the Russians). His death during the siege however allowed the Russians to make the decision to surrender the port which allowed General Nogi Maresuke's army to reinforce the Japanese forces in the Battle of Shenyang. According to Paine, if the siege had continued and Nogi's army failed to support Japanese forces at Shenyang there's a real chance the Japanese would've lost, which would have turned the war decisively in the Russians favour. Nogi seems to be aware of this, requesting to the Emperor to commit suicide for the high causalities his army sustained but was rebuffed.

Russia had the military means to continue the war - they had during the war deployed around 40% (788,000 men) of its army to fight Japan whilst Japan had deployed pretty much its entire army (670,000). Although the 1905 revolution and Battle of Tsushima had sapped support for the war in Russia, Japanese leaders believed Russians would not accept a Japanese-imposed peace unless it pushed westward into Russia which was considered an unfeasible prospect. Yamagata Aritomo, one of the most influential members of the Imperial Japanese Army, surmised the view within Tokyo that pushed for a mediated peace from outside powers

First, while the enemy still has powerful countries within its home country, we have already exhausted ours. Second, while the enemy still does not run short of officers, we have lost a large number since the opening of the war and cannot easily replace them...we must be prudent.

Russia only accepted peace talks if territorial annexations and an indemnity were off the table. Given Japan was entering talks in a position of supposed strength - having won every battle and Russia still in revolution - that time was the best to come to the table as attempting to persuade Russia to change its mind would risk Russia regrouping and potentially dealing a defeat to Japan, weakening Japan's negotiating position.

Unlike during the First Sino-Japanese War - and later during the second world war - military leaders did not push for excessive demands from the Russians, probably as they knew their forces could barely win another battle. This bucked the general trend of imperial Japanese politics of the military demanding excessive concessions from civilian politicians - during the Portsmouth negotiations military officials pushed against civilian politicians attempting to push through demands such as annexing the entirety of Sakhalin. The demands of the Japanese were modest enough that it was politically acceptable for St Petersburg to agree to them - Russia wanted to end the war and the treaty was a good way to save face with relatively light concessions whilst the Japanese basked in the glory of "defeating" a major European power.

The Treaty actually exceeded Japanese strategic objectives for the war - Japan had gone to war to retain influence in Korea alone but had ended up annexing south Sakhalin and Port Arthur whilst gaining influence in southern Manchuria in particularly administrating the South Manchurian Railway, which ended up being far more profitable then an indemnity would have been (and served as a launchpad in Japan later dominating and eventually colonising Manchuria). The Treaty was seen as "lenient" as the Japanese public - believing they had sacrificed so many men and won every battle - deserved more "spoils of war", a belief nurtured by the anti-American navy and revisionist army for whom Theodore Roosevelt became a convenient scapegoat for "denying" Japan the victory they felt they had fought for, a feeling intensified after the USA similarly intervened to prevent Japan breaking off sections of Siberia during the Japanese intervention in Siberia from 1918-1922. The precariousness of the Japanese army during the last stages of the war was forgotten as would open uncomfortable truths about the war - that it was more a Russian defeat then Japanese victory - that both civilian and military leaders were unwilling to stand by.

Source - Paine, S. (2017). The Russo- Japanese War (1904– 1905). In The Japanese Empire: Grand Strategy from the Meiji Restoration to the Pacific War (pp. 49-76). Cambridge: Cambridge University Press. doi:10.1017/9780511997662.004