Both say that you retain your proficiencies, so if you have proficiency in CON saves with a +10, you still have +10 on your CON saves in your new form, assuming the new form has the same CON modifier. At least that's how DnDB's char sheet behaves, but the char sheet's behavior is not a reliable source for rulings. In fact, it's completely broken.
On the right side you have the original stat block of a Deva, and on the left side, what it looks like in the char sheet if you add it as a shape-shift on a level 20 Sorcerer (so PB +6) who has proficiency in CON and CHA saves.
The +10 in CON saves, +5 in WIS and +11 in CHA saves imply that you get both your proficiencies AND also those of the new form, and those proficiencies use your PB. But somehow the stat block still indicates a PB of +4, which looks like an oversight. This in turn should also affect the Spell Save DC and attack rolls of your new form.
That Spell Save DC and spell attack bonus are already affected if your spellcasting ability modifier is different from that of the new form (and it should, otherwise keeping your mental stats would be pointless) since you get to keep that too, but if you also get to keep your PB as part of your proficiencies, it will also the affect other attacks of the stat block.
And that's where the char sheet completely breaks, because in spite of all these implications, besides what I've already shown, the rest of the stat block is completely unaffected (including the Spell Save DC), no matter how different your new stats are. My guess is that it's probably because making that work would imply rewriting every single stat block in the Monster Manual to make it scale properly. They must have had a way to make it work with the attributes' table, but not with the rest.
The character sheet doesn't actually support dynamic stat blocks like this; you appear to be getting that from the Beyond20 extension. If it's not calculating something correctly, that's something to take up with the Beyond20 developers.
But the answer to the question "Do you keep your Proficiency Bonus when using Shapechange?" is No. "Proficiencies" in the list of features you keep refers to the things you're proficient in, not the Proficiency Bonus itself.
This is a question about Shapechange and the Boon of Fluid Forms.
Both say that you retain your proficiencies, so if you have proficiency in CON saves with a +10, you still have +10 on your CON saves in your new form, assuming the new form has the same CON modifier. At least that's how DnDB's char sheet behaves, but the char sheet's behavior is not a reliable source for rulings. In fact, it's completely broken.
On the right side you have the original stat block of a Deva, and on the left side, what it looks like in the char sheet if you add it as a shape-shift on a level 20 Sorcerer (so PB +6) who has proficiency in CON and CHA saves.
The +10 in CON saves, +5 in WIS and +11 in CHA saves imply that you get both your proficiencies AND also those of the new form, and those proficiencies use your PB. But somehow the stat block still indicates a PB of +4, which looks like an oversight. This in turn should also affect the Spell Save DC and attack rolls of your new form.
That Spell Save DC and spell attack bonus are already affected if your spellcasting ability modifier is different from that of the new form (and it should, otherwise keeping your mental stats would be pointless) since you get to keep that too, but if you also get to keep your PB as part of your proficiencies, it will also the affect other attacks of the stat block.
And that's where the char sheet completely breaks, because in spite of all these implications, besides what I've already shown, the rest of the stat block is completely unaffected (including the Spell Save DC), no matter how different your new stats are. My guess is that it's probably because making that work would imply rewriting every single stat block in the Monster Manual to make it scale properly. They must have had a way to make it work with the attributes' table, but not with the rest.
The character sheet doesn't actually support dynamic stat blocks like this; you appear to be getting that from the Beyond20 extension. If it's not calculating something correctly, that's something to take up with the Beyond20 developers.
But the answer to the question "Do you keep your Proficiency Bonus when using Shapechange?" is No. "Proficiencies" in the list of features you keep refers to the things you're proficient in, not the Proficiency Bonus itself.
pronouns: he/she/they
Beyond20 adds shortcuts and QoL features, but it doesn't change any stats. I've double-checked just to be sure.
It's still doing that after deactivating the extension. That's DnDB's doing.