If I hidden a card and pass my turn, can I react to opponents or battlefield's beginning phase trigger right after?

To answer your question: Yes, you can react to beginning-of-phase triggered abilities, provided the trigger condition is met and it is not the same turn you hid the card.

Clarification on Reacting to Triggers

Triggered abilities (including those that trigger at the beginning of a phase, such as "At the beginning of your turn...") are placed on the chain as pending items. According to Rule 401.1 and Rule 309, adding an item to the chain creates a Closed State. Once the trigger is on the chain, it grants a reaction window, allowing players to play [Reaction] cards.

You cannot react to the beginning of the phase itself (because phases do not use the chain), but you can react to any triggered abilities that occur as a result of that phase beginning, because those abilities create a chain and a reaction window.

Timing Restrictions for Hidden Cards

Regarding your specific situation:

1. "Not the same turn" Rule: As specified in RiftJudge FAQ #790 and FAQ #8114, you cannot play a hidden card on the same turn that you hid it.
2. Playing from Hidden: Once it is a subsequent turn, you may play the hidden card. Because the card gains the [Reaction] keyword while facedown (Rule 811.6), you can play it in response to your opponent's triggered abilities.

Sequence of Events

If an opponent's card has a triggered ability that occurs at the beginning of their turn:

1. Start of Turn: The phase begins. No reaction window exists here.
2. Triggering: The triggered ability condition is met (e.g., "At the start of your turn...").
3. Chain Formation: The ability is placed on the chain as a pending item, creating a Closed State (Rule 401.1).
4. Reaction Window: Because a chain now exists, the state is Closed. You may now play your hidden card as a [Reaction] to that ability, provided it is not the same turn you hid it.

In summary: You cannot react to the start of the turn, but you can react to triggered abilities that occur at the start of the turn. You may use your hidden card to do so, provided the card was hidden on a previous turn.