Can a Shadow Weapon be used as Sword College bard’s spellcasting focus?

Question

Let's say I have a College of Swords bard (Xanathar's Guide to Everything, p. 15) that uses the Magical Secrets feature to learn the shadow blade spell and add it to the bard's spell list.

At level 3, College of Swords bards get the Bonus Proficiencies feature:

When you join the College of Swords at 3rd level, you gain proficiency with medium armor and the scimitar.

If you're proficient with a simple or martial melee weapon, you can use it as a spellcasting focus for your bard spells.

The text of shadow blade (Xanathar's, p. 164), which only requires vocal and somatic components, reads:

You weave together threads of shadow to create a sword of solidified gloom in your hand. This magic sword lasts until the spell ends. It counts as a simple melee weapon with which you are proficient.

While I am concentrating on this spell, would I be able to use this sword as a spellcasting focus for other spells that require material components?

Answer 1

Yes

It counts as a simple melee weapon with which you are proficient.

+

If you're proficient with a simple or martial melee weapon, you can use it as a spellcasting focus for your bard spells.

As written, the Shadow Blade satisfies the requisites for being used as a spellcasting focus. The text from College of Swords does not require it to be an actual/physical weapon, simply a melee weapon with which you are proficient.