Democrats hold 48 seats in the Senate, Republicans 50, with the two remaining seats belonging to Independents. I understand that Kamala Harris is a Democrat and can cast a tie-breaking vote, but her power is limited to just that. Thus, don't Republicans still hold more seats than Democrats (50 > 48), making Schumer the minority leader and McConnell the majority leader?
floor leaders - The majority leader and minority leader are elected by their respective party conferences to serve as the chief Senate spokesmen for their parties and to manage and schedule the legislative and executive business of the Senate. By custom, the presiding officer gives the floor leaders priority in obtaining recognition to speak on the floor of the Senate.
When the Senate meets at the beginning of each Congress (January 3rd of odd-numbered years), the Senators join one of two conferences. Each conference selects a floor leader. The conference with the largest number of Senators is the majority conference, the other is the minority conference. When the membership changes during the Congress, the roles of the majority and minority may reverse. With each new Congress and any reversal of roles, a vote for president pro tem is held. The president pro tem is the presiding officer for day-to-day meetings of the Senate.
In the case of an even number of Senators in each conference, the vote for president pro tem determines the majority conference. The vice president, using a tie-breaking vote, selects the nomination of their same party conference to become president pro tem. (There is rarely an actual vote.)
Why is Chuck Schumer considered the Majority Leader if the Democrats don't have a majority?
On January 20, 2021, neither conference held a majority, a resolution S.Res.6 was brought to the floor, and adopted by unanimous consent, making Patrick Leahy (D-VT) the president pro tem of the Senate.
When Leahy became president pro tem, Schumer (D-NY) became majority leader.
Because the two independents voted with the democrats for leadership of the senate resulting in a tie vote that was broken by the vice president.
To more directly answer the question of why Democrats are considered the "majority" party in the Senate (and thus, why Schumer is considered the Majority Leader,) it's because the two technically "independent" Senators (Bernie Sanders from Vermont and Angus King from Maine) caucus with the Democrats and, as such, agree to vote in favor of Democratic Senate leadership and are appointed to Democratic seats on Senate committees. This leaves the Senate with a 50-50 balance in practice. In cases of 50-50 ties, the tie-breaking vote is cast by the Vice President, which, as of Jan 20, 2021, is now Democrat Kamala Harris. This effectively gives Democrats control of the chamber, thus they are officially considered the "majority" party even though there is technically no majority in a 50-50 divide.
While not identical, this is somewhat analogous to how governments are formed in governments with larger third-parties in other countries. In those systems, two or more parties can agree to work together to form a coalition government with a majority of votes in parliament, even if none of the parties individually wins a majority of seats. Smaller members of the coalition are typically given certain concessions (such as leadership positions) in exchange for supporting the larger party in the coalition's candidate for Prime Minister.
In the case of Bernie Sanders, he's actually farther left than all but a few Democrats in Congress. He considers himself to be a Democratic Socialist. By 'independent' he does not at all mean 'moderate.' Indeed, he has (at least) twice run for President of the United States as a Democrat. In both 2016 and 2020, he secured (by a wide margin) the 2nd highest number of delegates for the Democratic Party's nomination and, per appointment by Senate Democrats, currently serves as the Chairman of the Senate Budget Committee. He's very much affiliated with the Democratic Party, but prefers to be officially considered an independent.
Angus King, on the other hand, is more center-left. Maine is generally known for preferring more moderate candidates and running as an independent helps Senator King to portray himself as a moderate during elections there. The Senior Senator from Maine, Susan Collins, is also generally considered to be one of the most moderate Republicans in Congress. In 2014, Sen. King even endorsed Sen. Collins' re-election bid. However, with policy positions more favoring the Democrats than the Republicans, he has chosen to caucus with the Senate Democrats, which gives them 50 votes (plus the Vice President) for Senate leadership purposes.