The Gallipoli campaign has come up here several times; while you wait for a new answer, you may also be interested in reading these older threads.

• In particular, this AMA with u/MargaretHarris is outstanding: AMA: the Gallipoli Campaign of World War One (and what/how various countries remember about it)

• Everything I have read has said that the attempted invasion of Gallipoli and the Battle of the Somme were misguided and served no real purpose other than to get men killed.

• What was the tactical advantage of storming Gallipoli?

• Which Narrative of Gallipolli is Correct?

The Gallipoli landings were basically the product of mission creep. The original conception was based on the fact that the British fleet had a whole bunch of slightly outdated ships that wouldn't have been of much use in the Atlantic and weren't serving much of a strategic purpose in the Mediterranean beyond bottling up the woefully outgunned central powers ships which couldn't do much anyways.

Given the stalemate on the Western front, a group in the British cabinet known as the "Easterners" wanted to try to win the war somewhere other than France and Belgium. One such idea (there were alternatives) was to try to capture Constantinople and knock the Ottomans out of the war.

The original idea for this was that those ships that I mentioned before would "force the straits". That is, plow through the Dardanelles, despite the heavy Ottoman defenses, accept whatever losses may come and hopefully a large enough portion could break through into the sea of Marmara and force Constantinople and the Ottomans to surrender.

It was eventually decided that a ground expedition should be put ashore to silence the artillery batteries along the Dardanelles while the ships forced the strait. But the British navy suffered significant losses, including three battleships sunk from mines on 18 March.

As a result, what had been conceived as a naval operation with ground support became a ground invasion with naval support: Gallipoli.

As to the wider strategic aims that you mention:

Was it true that the allied landing at Gallipoli was an attempt to...resupply the Russians?

I'm not sure that's quite how I would phrase it. The British and the French were already supplying the Russians via Arkhangelsk and Murmansk. But had the Ottomans been knocked out of the war you certainly would have had an easier time shipping those supplies, you would have had Russian and Commonwealth forces able to link up in the Balkans, and you would have freed up all the troops fighting in the Caucuses campaign for Russia, Mesopotamia for the British and defending the Suez Canal.

So that's a lot of troops, and a strategic objective significant enough that people have been arguing about the merits of the Gallipoli campaign ever since.

Unfortunately, I for one, am not convinced by any of the assumptions that underpin that line of reasoning. I'm not aware of any evidence that the Ottomans would have surrendered had the straits been forced. It's unclear to me what the British navy could have done to compel the Ottomans to surrender (what were they going to do? Shell Constantinople and commit an enormous war time atrocity?) Defenders of this view also tend to take a bit of a "lost cause" attitude, that if only there had been a bit more of a push, or one more go with the fleet, they could have won it.

I am incredibly skeptical of that. Gallipoli was a disaster from start to finish, and I don't think victory was close.