Hi, Gutenberg is ordering the tags alphabetically after saving, I don't want it to sort the tags, I need the tags in the order that I put them, I don't want it to sort it automatically.

This seems to be general WordPress behaviour, rather than specific to Gutenberg, and is the same in the classic editor.
How are you using the tag order? Your theme can show the tags in any order it wants, and this will appear in your post. How it appears in the editor shouldn't change that.
I have a plugin of related posts by tag, but the relation is not relevant because first look for the posts with the first tags stored alphabetically, and not the first main tag, that is to say for me the order of the tags are key because the first tag is the most relevant. So when saving everything, it is sorted alphabetically and this does not help me, any idea how to alter this?
The terms only seem to be shown alphabetically visually, but are stored in order added in the database, so I think this is really a design issue rather than a data one. It's a question of whether the best user experience is for this field to show the tags in order added or alphabetically.
That the tags are reordered on saving the post seems unusual to me.
I'll add the Needs Design Feedback label.
According to the database structure, I currently find it complicated that this can be ordered according to the order of the user.
What occurs to me that the IDs of the terms are stored in a wp_postmeta (only the ids) in a meta called '_tax_post_tag_orden' = 23,11,1,50 then this would have the order and with that you could play around a bit, for another tax without hierarchy the meta would be '_tax_mycuscomtax_orden' = 99,119,3,33 I suppose that there must be a filter at the moment of saving the post tags to be able to save this new wp_postmeta.
So when calling any function that has to do with tags, you can call the new parameter 'order' that will call the field '_tax_tag_orden' and return the IDs terms of this metapost.
$tags = get_tags(array(
'hide_empty' => false,
'order' => 'entered' // <= new param*
));
It is an idea but I think that there should be the possibility that the entered tags have the order entered. This greatly influences the related posts of plugins and themes since the first term would be the most prominent of the others.
If someone set a specific order, I think expecting them to stay in that order makes senses. I would vote to not reorder.
You just have to add a function just after saving in, this function saves in the wp_postmeta table a meta called _tax_{taxonomy}_orden and as value the IDS of the terms ordered as the user put them.
I've reworded the title of this so that it can be treated as an enhancement.
I faced the same issue and saw that while there is the wp_term_relationships table, it doesn't get properly updated with the tags' order on post update. As a workaround, I hooked into the rest_after_insert_this-post_type to update the order manually. Here is a more detailed explanation of what I did, along with some code that seems to work fine so far.
BTW, as I mentioned on #22048 , having an option to reorder terms with drag-and-drop would be great. Additionally, for better accessibility, there could also be complementary navigation using arrows. Here's a very rough sketch to get the idea of what I mean:

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If someone set a specific order, I think expecting them to stay in that order makes senses. I would vote to not reorder.