Is BTC inherently much more energy-hungry than other currencies, or just been around longer? A beginner question, but my understanding is that BTC (and many others) rely on solving ever increasingly complex algorithmic problems, which acts as a self-gating mechanism on the ever-decreasing cost of CPU power(?)
BTC's energy use has been in the news a lot recently and there's discussion about relative transaction cost in other coins. Do they work fundamentally differently, or is their blockchain just so much smaller that they are where BTC was, say, 2 years ago?
Or am I confusing mining with transaction cost?
other coins. Do they work fundamentally differently,

To secure the record of transactions, Bitcoin uses a type of mechanism called Proof of Work (PoW). Some other cryptocurrencies use any of several other mechanisms such as Proof of Stake (PoS).

BTC (and many others) rely on solving ever increasingly complex algorithmic problems

The complexity is not increasing. A &quot;difficulty&quot; target is adjusted that affects the number of iterations required. That difficulty target can go down as well as up.

BTC's energy use ...

The energy consumption of Bitcoin's PoW depends on the amount of computing power that miners have invested in. To ensure that new technologies and miners with deep resources do not become able to forge the transaction journal, Bitcoin increases the difficulty of Mining proportionally to the total computing power applied by miners. Mining is competitive so more powerful mining equipment provides a higher proportion of the rewards. So the energy consumption of the Bitcoin network is largely a reflection of the return on investment (ROI) that miners predict in their business plans. It isn't affected directly by number of transactions.
Transactions provide a transaction fee to miners, so the transaction rate and fee-rate has some influence on ROI.  However the transaction rate does not directly drive energy costs in the network.
To put it another way, if all but ten† miners left the Bitcoin network and those ten† only used one† small† PC each for mining, the transaction rate might not be affected and energy costs would be far far smaller. However, in the absence of any other limiting mechanism, the network would be insecure, a miner could step in and use overwhelming computing power to commit fraud.

† These numbers are not real, just illustrative. there is some minimal number that would be adequate to process current transaction rates if all humans were always honest, trusted all other humans in all circumstances, never had disagreements and never made mistakes. However Bitcoin was made for the real world and this requires some energy be expended to keep money secure