Difficulty adjustment plays into it but not super relevant since the security budget usually refers to tx fees

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And block subsidy when compared to the costs of mining. If difficulty drops, does it not become cheaper to mine the blocks?

It becomes easier. Not necessarily cheaper.

So then is the security budget issue real? If not many transactions occur on L1 and fees stay at 1 sat/vbyte combined with a reduced block subsidy, wouldn't that be a major issue?