Connecting dots from reporting by Reuters, BBC, DW, and NHK:

1. General Tiani, the leader of the Niger coup, was posted for twelve years as the commander of the Presidential Guard.

2. By all accounts, Niger is "rife with corruption".

3. President Bazoum was seeking to replace Tiani.

4. The previous President, who promoted Tiani to General and gave him his post, is also the father of the Oil Minister.

He has been critical of President Bazoum's handling of the Oil Ministry and other attempts to replace cronies of the former regime.

Likely scenario: General Tiani was making a small fortune from graft by leveraging his position. When new President Bazoum actually tried to curb corruption, Tiani became a target. Hearing this, Tiani reached out to other members of the military for support in a coup. Some of them agreed, as they were also profiting from corruption and therefore targets for President Bazoum's anti-corruption actions.

Since Niger is bounded on the East and West by countires under military dictatorships, on the North by the Sahara Desert, and the South by Nigeria and Benin, they need alliances with other generals (and Russia) to protect their borders.
As a former French colony, the Junta leaders can get popular support by blaming colonialism for all their economic troubles (4th from the bottom on a world scale) - nevermind that they receive over $200M a year in foreign aid, and have are heavily in debt to the World Bank. Their biggest export is Uranium, from two French-owned mines.

It looks like they are going to get in bed with Putin, who has mercenary relations (and mineral smuggling operations) through his lap dog Pregoshin with bordering Mali, Burkina Faso, and Sudan. "Citizen protests" supporting the coup have been waving Russian flags. Now what would Putin want with Uranium? What can he offer a country suffering from drought and high food prices?