Does Blue Sentinel trigger the hold effects of a battlefield for a second time or only the hold effects of units and gear present at the battlefield?

Yes — Blue Sentinel doubles the battlefield's own hold effect too, not just units' and gear's.

Blue Sentinel's passive reads "Your hold effects for holding here trigger an additional time" — it doesn't restrict to unit or gear abilities. "Hold effects" is a defined category (Rule 383.4.d) that includes any ability with a hold trigger condition, and battlefield abilities like Startipped Peak's "When you hold here, you may channel 1 rune exhausted" or Grove of the God-Willow's "When you hold here, draw 1" reference the player who held, so they qualify. Each triggers twice while Blue Sentinel is present at that battlefield (RiftJudge FAQ #10814 and #9697).