The "Halving"
in my experience ..only had a very small influence on the Bitcoin price.. just a week or a few days before it happens. The media attention in the weeks before the Halving, cause some hype in the markets.. but it is actually insignificant.
The Halving are definitely not a trigger for a new ATH, so I do not know where you have seen that.
The previous spikes in the price to a new ATH, was events like the ICO explosion on social media and large countries accepting Bitcoin as legal tender.
the actual effects are delayed by upto a year due to how the big industrial miners operate their accounting/costbase
they dont pander to daily price whims nor react to social drama's they have hardware lifecycles of 2+ years and electric contracts of 6month-2 years so they mine no matter what. and when its time to upgrade hardware/renew electric contracts (periodically) they look at how much coin accumulation vs cost. to then set their sell rates of previous periods accumulation
selling previous period accumulation while building up current/next period accumulation
(unlike home/hobby miners that can save money by just switching off asics as they pay monthly and so can save on electric bills and be on the market buy sentiment when prices are low)
the ATH have had more links correlation to mining activity than to social drama
EG
2011 was GPU pooling ramp up of costs compared to previous years solo CPU costs
2013 was first asic ramp up of costs compared to previous years of GPU costs
2016 was next gen asics (from ghash to thash)
2020 was next gen asics (over 100thash on small nm chips of only a could kwh)
those things changed the dynamics of how profitable/costly it was to mine meaning changing mindsets if people should mine to sell, vs market-buy low to sell high
changing the market sentiment
thers some economics dynamics at play
EG first release of next gen mining hardware only benefits the first delivery recipients with better efficiencies where they dont get hit by halving cost changes(lower cost plus more hashpower gives them best overall position). and it takes months-year for majority of network to upgrade to gain efficiency. by which time the hashrate has then climbed which then outpasses that initial efficiency gain of that first delivery recipient so then everyones costs go up due to the higher hash competition thus its about a year later before the true extent of the halving has settled into the new higher cost brackets
EG
if it costs say industrial iceland $16k to mine..
if it costs say industrial america $19.5k to mine..
if it costs say residential iceland $26.5k to mine..
if it costs say residential america $29.5k to mine..
if it costs say industrial europe $32.5k to mine..
.. and so on
if it costs say residential hawaii $90k to mine..
you can then start to see the sentiment zones of bitcoiners "switch" from hobby miner to personal buyer
(in industrial miners case they still mine. but if they have excess cash they buy while cheap too(when its cheap))
you can see that hawaii(germany/japan near that top too), if they have a good bitcoin community(population count) they are always going to be on the market buy sentiment as its always cheaper to buy rather than mine
so they are the ones remaining in the markets willing to buy even when the market is high. where as iceland are on a mega selling experience at that same high