Jelly, 11 bytes

Ẇ;Ɲw@Ƈ¥ÐḟṪL

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How?

Ẇ;Ɲw@Ƈ¥ÐḟṪL - Link: A, B
Ẇ           - sublists of A (from shortest to longest)
       Ðḟ   - filter discard those for which:
      ¥     -   last two links as a dyad, f(substringOfA, B):
 ;Ɲ         -     length 2 sublists of substringOfA
     Ƈ      -     keep those (pairs) for which:
   w@       -       is this pair a sublist of B?
         Ṫ  - tail -> longest uncommon substring
          L - length

Jelly,  11 10  9 bytes

-1 using ovs's observation.

;Ɲẇ€ṣ1ẈṀ‘

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10 byter

Ẇ;ƝẇƇ¥ÐḟṪL

Try it online!

How?

Ẇ;ƝẇƇ¥ÐḟṪL - Link: A, B
Ẇ          - sublists of A (from shortest to longest)
      Ðḟ   - filter discard those for which:
     ¥     -   last two links as a dyad, f(substringOfA, B):
 ;Ɲ        -     length 2 sublists of substringOfA
    Ƈ      -     keep those (pairs) for which:
   ẇ       -       is this pair a sublist of B?
        Ṫ  - tail -> longest uncommon substring
         L - length

Jelly,  11  8 bytes

-3 using ovs's observation!

;Ɲw@€TIṀ

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11 byter

Ẇ;Ɲw@Ƈ¥ÐḟṪL

Try it online!

How?

Ẇ;Ɲw@Ƈ¥ÐḟṪL - Link: A, B
Ẇ           - sublists of A (from shortest to longest)
       Ðḟ   - filter discard those for which:
      ¥     -   last two links as a dyad, f(substringOfA, B):
 ;Ɲ         -     length 2 sublists of substringOfA
     Ƈ      -     keep those (pairs) for which:
   w@       -       is this pair a sublist of B?
         Ṫ  - tail -> longest uncommon substring
          L - length

Jelly, 11 bytes

Ẇ;Ɲw@Ƈ¥ÐḟṪL

Try it online!

How?

Ẇ;Ɲw@Ƈ¥ÐḟṪL - Link: A, B
Ẇ           - sublists of A (from shortest to longest)
       Ðḟ   - filter discard those for which:
      ¥     -   last two links as a dyad, f(substringOfA, B):
 ;Ɲ         -     length 2 sublists of substringOfA
     Ƈ      -     keep those (pairs) for which:
   w@       -       is this pair a sublist of B?
         Ṫ  - tail -> longest uncommon substring
          L - length

Jelly, 11 bytes

Ẇ;Ɲw@Ƈ¥ÐḟṪL

Try it online!

Jelly,  11  8 bytes

-3 using ovs's observation!

;Ɲw@€TIṀ

Try it online!

11 byter

Ẇ;Ɲw@Ƈ¥ÐḟṪL

Try it online!

How?

Ẇ;Ɲw@Ƈ¥ÐḟṪL - Link: A, B
Ẇ           - sublists of A (from shortest to longest)
       Ðḟ   - filter discard those for which:
      ¥     -   last two links as a dyad, f(substringOfA, B):
 ;Ɲ         -     length 2 sublists of substringOfA
     Ƈ      -     keep those (pairs) for which:
   w@       -       is this pair a sublist of B?
         Ṫ  - tail -> longest uncommon substring
          L - length