Encode ASN.1 PKCS#8 Private Key with Public Key and attributes
This is more about representation and manipulation of data in a computer program than cryptography. Questions about Dart or the use of libraries in Dart, are better asked on Stackoverflow.
The [0] and [1] are context-specific tags; more exactly they are tags that are not universal (because then the number-type mapping would be fixed and known) with a class that is not specified and thus defaults to context-specific.
Because they are IMPLICIT, the top-level ASN.1 type of their contents is not encoded, and cannot be shown by a generic decoder like the one you link -- see a page earlier, above the table of universal types.
[0] is Attributes which in rfc5958 (and many other places) is SET OF Attribute (with infoset constraint) where CMS-style Attribute is SEQUENCE { attrType OBJECT IDENTIFIER, attrValue SET OF ANY --DEFINED BY type-- } in the old ASN.1 notation, or with attrValue defined by an infoset in the new notation. Thus the decode of [0] shows the one SEQUENCE of OID plus SET containing UTF8STRING.
On the other hand, [1] is PublicKey ::= BIT STRING which has no internal structure, so it is shown as raw data -- including the prefixed value octet for unused_bits = 00, so the real value of the publickey is the remaining 32 octets.