When the Vice-President is serving as Acting President on account of a temporary disability of the President, do they retain their Vice-Presidential powers, including the power to preside over the Senate and cast a tie-breaking vote?
The 25th amendment §3 says
Whenever the President transmits to the President pro tempore of the Senate and the Speaker of the House of Representatives his written declaration that he is unable to discharge the powers and duties of his office, and until he transmits to them a written declaration to the contrary, such powers and duties shall be discharged by the Vice President as Acting President.
Nothing in the Constitution deprives the Vice President of his powers / duties when he is also Acting President. Alternatively, the VP can become acting President under §4, without presidential cooperation, by declaration of the VP and a majority of the cabinet. Then either the President asserts that there is no inability, or Congress decides there is. But: unless the president dies or resigns, or is impeached, the VP is Acting President and actual Vice President, and therefore breaks ties in the Senate.
Note that under §4, the VP plus cabinet must declare POTUS unable, and must do it again if POTUS denies the inability. That means that there must still be a VP, who along with the cabinet re-affirms the disability.