Part of your question is asking if you can generate uuid in H2 right? I'm no expert, but it looks like you can:
http://www.h2database.com/html/functions.html#random_uuid
Second, you are asking if you can do this in liquibase similar to the way it is done targeting Postgres:
<property name="uuid_type" value="uuid" dbms="postgresql"/>
<property name="uuid_function" value="uid.uuid_generate_v4()" dbms="postgresql"/>
<column name="id" type="${uuid_type}" defaultValueComputed="${uuid_function}">
<constraints nullable="false" unique="true" />
</column>
Have you tried:
<property name="uuid_type" value="uuid" dbms="h2"/>
<property name="uuid_function" value="RANDOM_UUID()" dbms="h2"/>
<column name="id" type="${uuid_type}" defaultValueComputed="${uuid_function}">
<constraints nullable="false" unique="true" />
</column>
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