But on top of this, do they really need extra aid for this budget on top of the $3.3 billion that is already committed?
"Need" is a strong word. The Israeli GDP is over $500B, so the $3B, or even $30B, from the US are not critical. They can survive without it. But on the other hand, it definitely helps. Not only economically, but also politically - it's a strong show of support from a powerful ally.
To the US, on the other hand, it allows influence. The aid comes with strings attached. The aid (most of it) will be spent on US weapons (and of that - most in the US), or defensive weapons (like the Iron Dome). For example, look at these provisions in the HR8034:
$4.4B appropriated for spending in the US:
Provided, That the amount provided under this heading in this Act may be may be transferred to accounts under the headings “Operation and Maintenance”, “Procurement”, and “Revolving and Management Funds” for replacement, through new procurement or repair of existing unserviceable equipment, of defense articles from the stocks of the Department of Defense, and for reimbursement for defense services of the Department of Defense and military education and training, provided to the government of Israel
$5.2B appropriated for defense systems:
Provided, That of the total amount provided under this heading in this Act, $4,000,000,000 shall be for the Secretary of Defense to provide to the Government of Israel for the procurement of the Iron Dome and David’s Sling defense systems to counter short-range rocket threats: Provided further, That of the total amount provided under this heading in this Act, $1,200,000,000 shall be for the Secretary of Defense to provide to the Government of Israel for the procurement of the Iron Beam defense system to counter short-range rocket threats
$2.4B appropriated to the US military for its operations in the area:
2,440,000,000, to remain available until September 30, 2024, for transfer to military personnel accounts, operation and maintenance accounts, procurement accounts, research, development, test and evaluation accounts, and the Defense Working Capital Funds, in addition to amounts otherwise made available for such purpose, only for U.S. operations, force protection, deterrence, and the replacement of combat expenditures in the United States Central Command region
Finally, about $3.5B relatively unrestricted, but only $0.8B of it can be spent in Israel:
$3,500,000,000, to remain available until September 30, 2025, for assistance for Israel and for related expenses: Provided, That to the extent that the Government of Israel requests that funds be used for such purposes, grants made available for Israel under this heading in this Act shall, as agreed by the United States and Israel, be available for advanced weapons systems, of which up to $769,300,000 may be available for the procurement in Israel of defense articles and defense service
The influence is not only on how the money is being spent though. It allows the US government to add conditions on how weapons are being used, make decisions on what kind of weapons and ammunition would be provided under these funds, and obviously - allows exerting political influence.
If the Israeli Army is based on US equipment, it would depend on US supplies to maintain and use it, which in turn allows a certain level of "blackmailing" of the government. Not only when it comes to Palestinians, here's one example from a while back. Israel is in fact very technologically advanced, including in its military, and being able to control who can gain access to that technology is important to the US.
You also mentioned "$1 billion for additional humanitarian aid in Gaza", but that's not entirely true. The same bill includes these:
$9.15B for humanitarian needs:
$5,655,000,000, to remain available until expended, to address humanitarian needs, including the provision of emergency food and shelter, of vulnerable populations and communities
$3,495,000,000, to remain available until expended, to address humanitarian needs of vulnerable populations and communities:
Re "Ukraine seems to be in a rather difficult situation fighting Russia at the moment and probably needs more aid.":
The aid to Ukraine is very different from the aid to Israel. The type and amounts of weaponry provided to the Ukraine are very different. Ukraine doesn't need the Iron Dome, for example. It would have been very ineffective in that battlefield. It does need Patriot batteries, which Israel doesn't need as much. Ukraine doesn't need air-to-ground bombs and missiles for its barely functioning air force that Israel is getting, but it does need "dumb" artillery munitions and long range ground missiles that Israel doesn't. Ukraine needs tanks - Israel doesn't. Et cetera et cetera. So the aid is not really fungible.