What information does the bitcoin network & blockchain actually log about the miners themselves, such as hardware-specs/OS/hashing-rate/etc.?
None of that is logged. Miners may choose to make themselves publicly known, and/or to publish stats/information about their mining setups. But none of that is done at the network/blockchain level, in fact the bitcoin protocol requires no information from miners. Some miners choose to include some identifying information in the coinbase transaction extranonce, but there is no requirement to do so, and also no reason to assume that the information published there is in fact truthful, anyways.
As far as the bitcoin network is concerned, a miner simply needs to publish a valid block to the network in order to extend the chain.
So if you travelled back in time and wanted to participate as a miner, you would just need to submit a valid block to the network, which would be possible even if you were using modern ASIC hardware. All upgrades to the bitcoin network have been backwards-compatible soft forks, so you shouldn't have much trouble creating a historically valid block (though you could just run legacy software to create block templates, that you could then hash on using your modern hardware).
Note: given that the legacy network wouldn't be aware of soft-fork rule changes, you'd perhaps have to be careful about the sorts of transactions included in your block. For example, if you included a transaction that included segwit outputs, the other network nodes wouldn't understand the (modern) rules governing the spending of those transactions (ie, they would likely be stolen due to being 'anyone can spend' in the eyes of legacy nodes).
Would anyone even notice that something was odd?
Given the many-orders-of-magnitude improvements that modern ASICs have over legacy hardware, we'd expect that the time-travelling miner could likely find a majority of blocks extremely quickly, until the network difficulty adjusted to account for this. After a difficulty adjustment, the time-travelling miner would still assumedly find a majority of blocks, but at the expected rate of 10 minutes on average. Other miners on the network would notice, since their share of blocks would be greatly diminished (though it wouldn't necessarily be clear that this was due to a single new miner contributing a massive amount of hashpower).
If the time-travelling miner wanted to conceal their position of power, they could simply cycle their mining setup on and off, in order to not win 'too many' blocks.