We do not need to review these indicators unless the price drops below $25.5K, right?
Not quite. $25.5K is only the current mining cost (today's). Yesterday it was $20.4K, tomorrow it could be $30K. The issue would be price dropping below the average mining cost, whatever that may be at the time. What's always more relevant however has been the buy signal (when the hash rate recovers), as opposed to the capitulations. Sometimes the miner capitulations can be during healthy upwards price recoveries.
If the price drops to lower levels, the miners will not close the mining tools directly, which means that we may see the effect after two or three months and not directly.
If price drops below the average mining cost, you will inevitably see some miners switching off (more so than miners switching on). Of course this is subjective to where in the world you are mining.
In the US the average cost is reportedly the $30K level, so US miners are likely to switch off below this level (and switch back on above it), to avoid mining at a loss. For other countries, it could be $20K, even $10K, so they'd be switching more on if they can, especially if the mining cost reduces. Or with renewable energy, it could be substantially lower, though the cost of ASIC Miners still exists for the green miners.
During this period, if the price goes back up, will it cancel the effect?
More of less, but again this depends on the mining cost, hash rate, as well as difficulty. If the mining cost were to stay at $25K levels, and price then stays above $30K, then sure it's likely to provide a buy signal, as more miners switch back on. But without checking specifically at which hash rate level (and time-frame) the 30MA and 60MAs would crossover again, it's far from a certainty even if very likely.
Are miners affected by the daily or weekly changes in the bitcoin price? I thought they were investing in the long term.
To put it simply, yes. They aren't affected by the daily/weekly hash rate, but more so the difficulty that changes every 2 weeks. So if the difficulty decreases (and therefore costs reduced), it becomes more profitable to mine, and when it increases it becomes less profitable. If on one day the cost of a US miner is $30K, and price goes below it, then for sure these miners would likely switch off - until the price goes back above it.
While miners as an industry are known to sell large amounts Bitcoin when it is high, and avoid selling too much when it is low, it's just like any other business - it's about making profits, not hodling. This is where the phrase mining capitulation comes from. It's nothing to do with miners selling their BTC, but to do with miners switching off their machines because the cost of mining is higher than the current price.