Hypothetically, could the U.S. Congress abolish itself and transfer all power to the President? I'm thinking of a scenario where Congress amends the Constitution and gives all power the President, while also removing it's own power.

Theoretically Yes, but they couldn't do it on their own

Amendments to the US Constitution can change or overrule earlier parts without issue. For example, the 17th Amendment modified the part of Article 1, Section 3 which said that Senators were elected by the State Legislature, and replaced it with direct elections by voters in each state.

Therefore, there is no reason that a constitutional amendment couldn't make other fundamental changes, such as letting the President appoint Congress, or giving the President the ability to propose and approve bills.

However, even if they wanted to give up their power, Congress couldn't pass a Constitutional Amendment on their own. Article 5 of the US Constitution dictates a 2-step process for passing an amendment:

The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress;

First, an amendment must be proposed, either by passing both the House and the Senate with a 2/3 majority, or by being approved at a Constitutional Convention called by the states (which has never happened, after the original Convention).

Then, the amendment must be ratified by the State Legislature, or a state Constitutional Convention, in 3/4 (currently 38) states.

So, it wouldn't be enough for Congress to want to institute a dictatorship, the individual states would have to agree too.

There's one other limitation:

The last clause of Article 5 puts another limitation on constitutional amendments:

Provided that ... no State, without its Consent, shall be deprived of its equal Suffrage in the Senate

You could make an argument that abolishing the Senate would maintain equal Suffrage (every state gets the same 0 Senators), but any State that opposed this plan would almost certainly have grounds to sue to the Supreme Court on these grounds.

Hypothetically, could the U.S. Congress abolish itself and transfer
all power to the President? I'm thinking of a scenario where Congress
amends the Constitution and gives all power the President, while also
removing it's own power.

No.

Congress can proposed amendments to the U.S. Constitution, but it can't adopt amendments to the U.S. Constitution without approval from state legislatures. So, because Congress can't amend the Constitution, the answer is no.

Furthermore, Article V of the U.S. Constitution provides that:

no State, without its Consent, shall be deprived of its equal Suffrage
in the Senate

via a Constitutional Amendment. And, I do not believe that any fair reading of the U.S. Constitution would find that abolishing the U.S. Senate entirely would not violate this provision.

Since this is beyond the scope of a permitted constitutional amendment, the only way to secure your proposed change would be to violate the law and the constitution in some sort of coup or revolution (bloodless or otherwise) and to establish a new regime, much as the United States did when it extra-legally declared its independence from the British Monarch.

Congress also cannot pass a law that would do this because the non-delegation doctrine (a separation of powers concept that is part of U.S. Constitutional law) provides that a law that does not provide an "intelligible principle" to govern how it should be carried out is unconstitutional and void.