Replace string-matching error detection with typed SQLite errors

Use errors.As with *sqlite.Error and SQLITE_CONSTRAINT_UNIQUE code
instead of fragile strings.Contains(err.Error(), "UNIQUE") checks.

Add db.IsUniqueConstraintError helper in internal/db/errors.go and
replace all three string-matching call sites in api.go and auth.go.

internal/handlers/auth.go

@@ -4,6 +4,8 @@ import (
 	"encoding/json"
 	"net/http"
 	"strings"
+
+	"git.eeqj.de/sneak/neoirc/internal/db"
 )
 
 const minPasswordLength = 8
@@ -94,7 +96,7 @@ func (hdlr *Handlers) handleRegisterError(
 	request *http.Request,
 	err error,
 ) {
-	if strings.Contains(err.Error(), "UNIQUE") {
+	if db.IsUniqueConstraintError(err) {
 		hdlr.respondError(
 			writer, request,
 			"nick already taken",