Albert Einstein appeared to have two opinions on Zionism, and a lot of folks go back and forth on this because they think of Einstein as a person whose mind never changed.
In fact, part of the confusion is because Einstein's Zionism and anti-Zionism went back and forth multiple times, not only once.
For example, consider Niv Goldstein's article "Albert Einstein's early Zionist involvement, 1918–1920", in Israel Affairs. He catalogues Einstein's early impressions and later impressions as they grew. Einstein was, he says, entirely uninterested in Zionism in the early 1910s, when he first encountered it. In 1914, Einstein again encountered Zionists, and while he felt that Jewish solidarity was important, he was not necessarily a Zionist either. He began to see Jewish identity as important to maintain and uphold, but did not take a say on the method, i.e. creation of a Jewish state or not.
In 1918, when he wrote an essay on the rise of antisemitism, he mocked assimilationist Jews who believed that they could fight German antisemitism by insisting on their Germanness. He believed antisemitism was irrational, not something you could fight by pretending to be less of a Jew, less of a unique and separate group, because he believed no one would accept that about Jews. But he still did not adopt Zionism as an idea.
However, Zionists noticed his essay, and reached out later that year. And in discussions, they managed to get him to sign onto a declaration drafted that would endorse the right of Jews to a national home in what is now Israel. Whether this was understood by him to mean a state is unclear, but it certainly seems likely. Einstein, Goldstein writes, seems likely to have been reluctantly coming around to Zionism, believing that there was no solution to antisemitism in the world that could protect Jews so much as a state, and this troubled him greatly, being one of those Jews in the diaspora himself. He was a universalist and yet endorsing a Jewish political movement for a national home, another contradiction that troubled him. But still, in a letter in 1920 to a relative who asked him if he was an "ardent Zionist" as one paper had described him, he wrote:
Not much time has elapsed since I became a Zionist. But I nevertheless am happy about it. Our people will attain its own home, and the university that should be established in Palestine particularly interests me [my note: this was Hebrew University, which does exist]. They even say that I myself would like to move to Jerusalem; but that is a myth, like many other things that have been printed about me. I am both too old to master the Hebrew language, and it is almost entirely foreign to me.
But as with all things, this was not the end of the story. Einstein did describe himself as a Zionist, and did endorse a state, but things change. Einstein saw the ongoing conflict between Jews and Arabs in the area, which likely tugged him back towards his universalist goals. Thus, in 1938 or 1939, he seemed to take a step back and away from his Zionism. He gave a speech where he said:
I should much rather see reasonable agreement with the Arabs on the basis of living together in peace than the creation of a Jewish state. My awareness of the essential nature of Judaism resists the idea of a Jewish state with borders, an army, and a measure of temporal power, no matter how modest. I am afraid of the inner damage Judaism will sustain—especially from the development of a narrow nationalism within our own ranks, against which we have already had to fight strongly, even without a Jewish state...If external necessity should after all compel us to assume this burden, let us bear it with tact and patience.
What this means is somewhat unclear. He may have been endorsing a binational state, which some considered Zionism, but the complexities and details of that are hard to puzzle out. What is clear is that he wasn't necessarily endorsing a Jewish state here, and this does seem out of whack with his earlier proclamations of both Zionism and a Jewish state being something he supported. This likely, as I mentioned, stemmed from ongoing conflicts; in that period, there was an ongoing Arab revolt in Mandatory Palestine, and the British were attempting to quell it (eventually also issuing a White Paper limiting Jewish land purchases and immigration to the region in 1939, which lasted through the Holocaust and WWII). Einstein likely was concerned about this and felt, as I said, tugged back to his universalism.
But wait, there's more!
In 1947, after the end of WWII and the end of the Holocaust, Einstein was again endorsing the idea of a Jewish state, and even writing on behalf of it to foreign leaders. In 1947, for example, he sent a letter to Indian Prime Minister Jawaharlal Nehru, advocating for India to support the UN Partition Plan of 1947, which would have established a Jewish state. As he said:
Long before the emergence of Hitler I made the cause of Zionism mine because through it I saw a means of correcting a flagrant wrong.
Thus, he seemed both concerned always of Zionism overcorrecting, as he said in 1948 in a separate letter, but also believed it was a morally just cause to correct "a flagrant wrong".
I think it's fair to say he was a Zionist, and may have always remained one albeit a reluctant one at times, though perhaps at times he strayed away from it during times of particular strife. We can say, as far as I know, that he returned to full-throated belief that Israel should exist by 1947 without a doubt, and continued to say as much later on, to my knowledge, until he passed.