What's my TIO uniqueness? Try it online! currently has 680 listed languages, all of which are searchable. For most of those languages, when searching for it, you don't have to enter the entire string. For example, entering lega results in just 05AB1E (legacy) appearing, and entering d+ results in only Add++. However, for some languages, there is no such string that results in only that languages, e.g. Jelly returns both Jelly and Jellyfish
We will call the length of the shortest string required to return only a specific language on TIO the TIO uniqueness of that language. The TIO uniqueness of a language for which this is impossible is undefined. Note that TIO ignores case when searching, so bri results in Brian &amp; Chuck and SOM results in Somme.
You are to take the name of a programming language on Try it online!, exactly as spelt in the search function, and return that language's TIO uniqueness. If the language's TIO uniqueness is undefined, you may instead return any value which is not a positive integer (or could reasonably be interpreted as a positive integer). This value need not be consistent between such languages. Your program should handle all 680 languages currently on TIO.
This is code-golf, so the shortest code wins. Standard loopholes are forbidden, especially internet access. You may also not access the file system of TIO. Essentially, your program should work whether it's run on TIO or locally.
Test cases
All test cases include the TIO uniqueness string in lowercase, as TIO is case insensitive in its search, and use 0 for undefined TIO uniquenesses
&quot;Arcyóu&quot; -&gt; 1 (&quot;ó&quot;)
&quot;Befunge-98 (PyFunge)&quot; -&gt; 13 (&quot;befunge-98 (p&quot;)
&quot;Cauliflower&quot; -&gt; 3 (&quot;cau&quot;)
&quot;Shove&quot; -&gt; 3 (&quot;hov&quot;)
&quot;Funky&quot; -&gt; 0
&quot;,,,&quot; -&gt; 2 (&quot;,,&quot;)
&quot;Agony&quot; -&gt; 0
&quot;Starry&quot; -&gt; 4 (&quot;tarr&quot;)
&quot;Add++&quot; -&gt; 2 (&quot;d+&quot;)
&quot;ATS2&quot; -&gt; 3 (&quot;ts2&quot;)
&quot;F# (.NET Core)&quot; -&gt; 5 (&quot;f# (.&quot;)
&quot;Dyvil&quot; -&gt; 2 (&quot;yv&quot;)
&quot;Python 3.8 (pre-release)&quot; -&gt; 2 (&quot;3.&quot;)

The full list of names and the full list of test cases
JavaScript (Node.js),  819  779 bytes
Returns 0 for undefined TIO uniqueness.
s=&gt;(B=Buffer)('J .!&gt; . 8 &quot; .  . 0 L&quot;0&quot;c$E&quot;~~~=&quot;8&quot;~1 Y$^&quot;~~~j S$x&quot;P S$;&quot;7 @ Z G&quot;/$8$A :%X!T%A G M$c*h&quot;d&quot;L!Q$8&quot;~F$.$&gt;&quot;s$@&quot;`&quot;E 3 1$r&quot;U&quot;&gt;&quot;8 F&amp;~Y&quot;=&quot;z&quot;~Q&quot;F&quot;E&quot;g |&quot;R%m!c$&quot;~N&quot;~?$Q  1 ~W B$k&quot;F =&quot;d$&gt; U&quot;7%&quot;&quot;&quot;F&quot;X%Y%s&quot;S$E&quot;&lt;-O$b _&quot;]&quot;?$3 &lt;$B i&quot;0&quot;~A&quot;W&quot;&gt;$6 L `&quot;I%2&quot;1&quot;?$6&quot;M &quot;A _$2&quot;A =&quot;; T&quot;t @$:&quot;q&quot;N i&quot;[&quot;V&amp;~= z&quot;5&quot;1 I!N&quot;8&quot;Z ` ~~B 4&quot;1 }&quot;#&quot;2$.&quot;e P F ;!A&quot;W$K G&quot;&gt;$9$K&quot;T M*W #&quot;8 &lt; 0&quot;A ]&quot;&quot;~~J Z&quot;&quot;m&quot;0&quot;V!; ~~[ h+$2$~^&quot;1&quot;3$1&quot;3 A$}&quot;D&quot;~i&quot;9 H%N&quot;~3 9 K&quot;~4&quot;; C%C&quot;Q&quot;3&quot;/ X ^&quot;D&quot;9$4 4 /&quot;7 J&quot;:$$0*o&quot;~&lt;&quot;Z 9&quot;T&quot;I&quot;~D$5&quot;@ 1&quot;j &quot;. ~c&quot;O$4&quot;3 O ~X 6$K&quot;I ~8 F  d$T } 6&quot;#&quot;V&quot;W&quot;;$I$0 H$R&quot;x$&quot;[$6 j i&quot;U&quot;~M L&quot;K$~~h W$L O&quot;0%=&quot;Z 4&quot;F$X&quot;6!?$;&quot;4&quot;M&quot;~0$~1%r&quot;k&quot;6&quot;K&quot;^&quot;2 5$V v&quot;4&quot;J&quot;z 1&quot;1 H$;$W&quot;#&quot;&gt;!i&quot;.&quot;V&quot;V$e&quot;6$~~&lt;*~C!~/&quot;7 8!/ q$3&quot;U /&quot;.&quot;? t&quot;Y&quot;J!&lt;$4 i&quot;~P K&quot;Y'.replace(/[.-~]/g,c=&gt;'#'.repeat(B(c)[p=0]-44))[B(s).map(c=&gt;p=(p*79^c)&gt;&gt;&gt;0)|p%12635])[0]-32

Try it online! (test cases)
Try it online! (all languages)
How?
There are only \$10\$ distinct TIO uniqueness values, ranging from \$0\$ to \$13\$. Besides, more than 50% of the languages have a TIO uniqueness of \$3\$.
 uniq. | count | ratio
-------+-------+--------
   0   |   97  | 14.24%
   1   |   12  |  1.76%
   2   |  140  | 20.56%
   3   |  357  | 52.42%
   4   |   56  |  8.22%
   5   |   11  |  1.62%
   6   |    2  |  0.29%
  10   |    4  |  0.59%
  11   |    1  |  0.15%
  13   |    1  |  0.15%
We need:

a function \$H_0\$ that turns the language name \$s\$ into an integer \$H_0(s)\$
a function \$H_1\$ and a corresponding lookup table \$T\$ so that the TIO uniqueness of the language is \$T[H_1(H_0(s))]\$

It seems unlikely to find some simple functions \$H_0\$ and \$H_1\$ that would directly lead to a small lookup table. But if we use \$3\$ (the most common uniqueness) as the padding value for unused slots, the table is going to contain a lot of \$3\$'s.
So our strategy is to use:

the first 14 printable ASCII characters (32 to 45, i.e.   to -) to encode the actual uniqueness values other than \$3\$
all other printable characters (46 to 126, i.e. . to ~) to encode runs of 2 to 82 consecutive \$3\$'s

Conveniently, the single quote ' (ASCII code 39) will never appear in the table because no language has a uniqueness of 7. So we can use it as our string delimiter and safely use &quot; and ` in the table without having to escape them.
We now need to find \$H_0\$ and \$H_1\$ so that the distribution of actual uniqueness values among the \$3\$'s leads to the smallest table with this simple compression scheme.
After some brute-forcing, it turns out that the following functions work reasonably well:

Buffer(s).reduce((p, c) =&gt; p * 79 ^ c) &gt;&gt;&gt; 0 (actually implemented with a .map())
% 12635