Historically, China backed the monarchy (the royal family excluding Gyanendra never really forgave Nehru and Indira Gandhi for abolishing and then nationalizing royal property, as the Shah family continues to only marry Hindu royalty within their caste along with their historic antipathy to a monarchist Hindu Rashtra leading to the INC backing the Nepali Congress and Vanarasi-raised and ideologically Gandhian Koirala brothers) and KP Sharma Oli's Marxist communist faction, while India backed the Prachanda Path communists and the Nepali Congress (NC).
After the move to democratization, India continued to back NC and Prachanda (eg. He and his wife are/were devoted followers of BJP-aligned Baba Ramdev [0][1][2]), but KP Sharma Oli's faction continued to lean pro-China, as he and his peers started their revolutionary path during the Naxalbari uprising [3]. The monarchists (RPP) on the other hand switched to being more India leaning after Yogi Adityanath - the religious leader of the Gorakhnath Math which is heavily patronized by the royal family and Pahari Hindus from Kathmandu to Kashmir - became the Chief Minister of Uttar Pradesh.
Last year, the NC surprised everyone by collapsing Prachanda's government and making an alliance with KP Sharma Oli.
Based on how prominent Maoist Center (Prachanda), RSP, and RPP party workers have been during the protests and even within the discord, I am starting to suspect this was a repeat of the Rajapaksa-Siresena episode in Sri Lanka in the sense that a significant faction was used to undermine the China leaning Oli government.
Sushila Karki is viewed as fairy pro-India - the town she's from is for all intents and purposes Bihar, and she studied at the PoliSci department at Banaras Hindu University during the JP Andolan and when several future Indian political leaders were studying at BHU as well. China also hasn't congratulated her yet but the Indian government did almost immediately after the announcement. Of course, we will only find out once Karki's cabinet is announced.
[0] - https://english.khabarhub.com/2019/20/63249/
[1] - https://english.makalukhabar.com/ramdev-arrives-at-prachanda...
[2] - https://www.hindustantimes.com/world/prachanda-fellow-maoist...
[3] - https://ora.ox.ac.uk/objects/uuid:b959a806-fd27-4c20-bfb3-a2...