The absence of either battleship in Ten Go is rather easily explained. Neither Haruna nor Nagato were combat ready in March/April 1945. The two battleships were mostly repaired from the damages incurred during the Leyte campaign and its aftermath, but they were still not fully operational. But even more crippling than prior damage was the lack of fuel for these heavy ships.
The IJN had deactivated BatDiv 1- the designation for its surviving battleships- in 10 February 1945. The overarching reason was that there simply was not enough oil for these battleships to sail as a unit. Haruna and Nagato became coastal defense vessels assigned to Kure and Yokosuka respectively. Nagato for instance had a pier-based coal powerplant providing her partial power. Haruna was something of a sitting duck during TF 58's airstrikes on Kure on 19 March but she only received light damage.
Although Yamato too was assigned to Kure when BatDiv 1 was disestablished, she avoided Haruna's fate. For one thing, she was the most modern heavy surface combatant available to the IJN, so the Japanese did spend their scarce resources to keep her operational. The IJN had simply invested too much into her to redesignate her a coastal defense ship and start a long-drawn out process of landing her AA guns and other equipment, a fate which befell both Nagato and Haruna over the course of 1945. The IJN did not have enough fuel to keep the three battleships of BatDiv 1 operational, but it could sacrifice enough scarce oil to keep one battle-ready.
The IJN only barely had enough fuel though to keep Yamato in readiness. Contrary to received wisdom, Yamato was not given just enough fuel for a one-way trip to Okinawa. The logistics officers at Tokuyama were able to scrape up enough oil from the bunkers to give Yamato a bare fraction of fuel to almost make a return trip to the home islands if she did not engage in any excessive maneuvers. The Combined Fleet directed the fleet only to be supplied with 2000 tons of oil, but the Tokuyama's officers were able to scrounge up 8000 tons for the whole force. This extra margin allowed for the Ten-Go ships to engage in maneuver when they were under air attack as well as allowed the three surviving destroyers to pick up survivors and return to Sasebo.
But the herculean efforts to fuel Ten-Go's ships underscore the dire straits the IJN was in during the spring of 1945. There simply was not enough fuel to power a maximum last-ditch effort, so the IJN sent only what it could afford to in order to meet the Okinawan invasion.