Hi there JamFran,

as a 13th level Lore Bard, you'll have the following magical secrets features:

10th level (Bard class): Magical Secrets

Choose two spells from any classes, including this one. A spell you choose must be of a level you can cast, as shown on the Bard table, or a cantrip.

The chosen spells count as bard spells for you and are included in the number in the Spells Known column of the Bard table.

The choice of spells are made at 10th level, at which point the character can cast up to 5th level spells. As such, only 1st through to 5th level spells can be selected. There is no provision in this feature for re-selecting the spells at higher level.

6th level (College of Lore subclass): Additional Magical Secrets

At 6th level, you learn two spells of your choice from any class. A spell you choose must be of a level you can cast, as shown on the Bard table, or a cantrip. The chosen spells count as bard spells for you but don’t count against the number of bard spells you know.

The choice of spells are made at 6th level, at which point the character can cast up to 3rd level spells. As such, only 1st through to 3rd level spells can be selected. There is no provision in this feature for re-selecting the spells at higher level.

The Plane Shift spell is a 7th level spell, as you noted. None of the magical secrets class or subclass features your 13th level character has, allow the selection of this spell.

The D&D Beyond character sheet and builder reflect this correctly.

Please note that, when your character reaches 14th level, they will receive another magical secrets class feature, which will allow the selection of spells up to 7th level.

What I have stated above is definitely how our tools have defined it.

I am 100% sure you are actually correct though and will follow up on this!

As you say though, the Bard class includes this line under spellcasting:

Additionally, when you gain a level in this class, you can choose one of the bard spells you know and replace it with another spell from the bard spell list, which also must be of a level for which you have spell slots.

There's also this in Sage Advice

https://www.dndbeyond.com/sources/sac/sage-advice-compendium#SA011

Can a bard replace spells gained through Magical Secrets?

When you gain a level in the bard class, the class’s Spellcasting feature lets you replace one bard spell you know with another bard spell of an appropriate level. A spell learned through your Magical Secrets feature counts as a bard spell for you, so it can be replaced upon gaining a bard level later. But it must be replaced by a bard spell, according to the rule in the Spellcasting feature.

So ... sorry if it feels like I am flip-flopping on you here, but having fully read through the rules, and checked Sage Advice and other references, the specific spell Plane Shift would not be eligible, because it isn't a Bard spell.

As per the last sentence of that Sage Advice clarification I linked above.

I generally don't play Bards, so this has been a voyage of discovery for me too! 😊