The texture/model of crying obsidian is rotated randomly on Bedrock Edition. However, it is not randomly rotated on Java Edition, giving way to this parity inconsistency.
The random rotation of crying obsidian (as well as glowstone) can be seen at 5 minutes and 38 seconds in this ibxtoycat video: https://youtu.be/F4URvpHyov0
It may also be worth noting that there are several other blocks from before 1.16 which are similarly affected, namely coarse dirt, glowstone, obsidian, clay, terracotta, all stained unglazed terracotta, magma blocks, sponges, wet sponges, sandstone and red sandstone, which could be similarly fixed in conjunction with crying obsidian's case.
Also visible is the fact that the sides of said blocks are rotated in Bedrock Edition which does not at all happen in Java Edition. Again, this is a completely different parity issue which has existed before 1.16. Netherrack appears to have side rotation or flipping worked out, so its model could be applied to dirt, sand, gravel, and all the blocks from the above paragraphs (excluding sandstone and red sandstone) to achieve parity for these blocks.
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I feel like there are hundreds of parities between Bedrock and Java, and there have always been, as far as I'm aware. Even redstone works really differently in Bedrock compared to Java. Not entirely sure it's a bug so much as it's a difference in design, seeing as Bedrock is developed by a different team, or it could be a difference in functionality of the coding languages. I guess they're not too concerned with making sure all mechanics are exactly the same across all platforms.
This parity issue seems to be put in a gray area, since there are other instances of things rotating in Bedrock but not Java (and vice versa) that were implemented before Buzzy Bees. I still think this is a valid report, but random rotation parity as a whole needs to be looked at. I have noticed there are so many things that randomly rotate in Bedrock unlike Java, but despite this, Bedrock doesn't randomly rotate stone unlike Java.