Rosh Hashanah's concealed joy

בכסה ליום חגינו כי ר"ה בין המועדות כי לבנ"י הוא שמחה שלטובתינו נתן השי"ת ימי תשובה ומשפט בכל ר"ה להתנקות בעוה"ז מכל חטא.

"On the covered [moon] for the day of our festival" (Tehillim 81:4) — for Rosh Hashanah is among the festivals, since for Bnei Yisrael it is a joy that, for our own good, Hashem gave us days of teshuvah and judgment each Rosh Hashanah, to be cleansed in this world from every sin.

Rosh Hashanah is counted as one of the festivals because, despite its awesomeness, it is truly a cause for joy: Hashem in His kindness gave us a fixed time each year to do teshuvah and be purified of sin while still in this world.

ואמת שבנ"י בטוחין שיצאו זכאין וגמר השמחה הוא ניכר בסוכות.

And in truth Bnei Yisrael are confident that they will emerge meritorious in judgment, and the completion of this joy becomes evident on Sukkos.

Bnei Yisrael trust that they will be vindicated in the judgment of Rosh Hashanah; the joy that begins now reaches its full, visible expression later, in the simchah of Sukkos.

וזהו בכסה ליום חגינו.

And this is the meaning of "on the covered [moon] for the day of our festival."

The verse calls Rosh Hashanah a "festival," yet describes it as "covered" — the joy is real but still concealed, not yet openly revealed as it will be on Sukkos.

כי בר"ה יש קטרוג על זה שבנ"י מובטחין יותר ובזה מובן הגמ' למה אין אומרים הלל בר"ה כו' והבן:

For on Rosh Hashanah there is an accusation (kitrug) precisely over the fact that Bnei Yisrael are so confident; and with this we understand the Gemara's question as to why we do not recite Hallel on Rosh Hashanah — understand this.

Because Bnei Yisrael's very confidence in being acquitted could arouse a heavenly prosecution against them, the joy must remain "covered" and restrained. This explains why no Hallel is said on Rosh Hashanah: open, jubilant praise would expose that confidence to the accuser, so the simchah is kept hidden until Sukkos.

Summary: Rosh Hashanah is genuinely one of the festivals — a joyous gift of days for teshuvah and cleansing — and Bnei Yisrael are confident of a favorable judgment. Yet that very confidence invites accusation, so the joy must remain "covered" (bakeseh) and unspoken; this is why no Hallel is recited on Rosh Hashanah, with the joy reaching its open fulfillment only later on Sukkos.