Equinor is a cross listing which means the shares will be the same and it is the same legal entity. Prices should align in this case, unlike dual listings like Royal Dutch Shell (in the early 1980s, Royal Dutch was trading at a discount of approximately 30% relative to Shell).
However, you are looking at volatile time series at different times. The price you download (I assume, since you did not specify) is the closing price each day. There are a few hours difference between OSE close and NYSE change. Therefore, both the stock, as well as the exchange rate fluctuate and explain most of the difference between OSE and NYSE.
If you have access to Bloomberg, you can look at HVT to see intraday prices or download them via the API. To get the FX rates at specific times, it is best to use BFIX. If you naively convert the two series into NOK and plot it on Bloomberg you will also have a mismatch, albeit a lot less systematic than yours (in fact quite random and still small).
For example, the naive exchange rate conversion (BBG used BGN, a generic 5pm New York time composite price and as default in my case) and using simply the closing price for both exchanges produces a fairly large difference of 1.4% on the 8th of may 2023. Looking at a trade time that matches, and converting with BFIX into NOK, the difference turns into 0.2%. Even if both markets are open, you need to be careful when simply looking at the values. It is likely that you do not have access to real time data unless you use a trading system (it costs money to have access to real time data).
Therefore, I suppose the persistent gap you see is mainly a data quality issue on your side.
There will be some spread due to market frictions (bid ask spreads etc) that prohibits arbitrage, which is why small deviations can still exists.