Unable to inspect date in datepicker for automation

I am trying to automate a datepicker but when I tried to find the locator for an individual date, I'm not able to inspect it. I have attached a screenshot for HTML and the code I have tried is below. Code runs until it selects month, then it does not work. Even test also has passed, I don't know without selecting date how it can pass.

This is the link where you can find the date picker and html codes for locator : https://www.grangehotels.com/

public void datePicker() {
        driver = new ChromeDriver();
        driver.manage().window().maximize();
        driver.get("https://www.grangehotels.com/");
//        waitForElementToBeVisible(_coockies, 20);
        clickOnElement(_coockiesHomepage);
        clickOnElement(_bookARoom);
        selectFromDropDownList_ByVisibleText(_selectAHotel, "Grange Buckingham Hotel");
        clickOnElement(_checkinDateHomePage);

        // select date 05/05/2023
        String checkinDate = "05-May-2023";
        String monthYear = "May 2023";
        String date = "5";

        waitForElementToBeVisible(_monthHeading, 50);
        while (true) {
            String monthYearHeading = getTextFromElement(_monthHeading);
            if (monthYearHeading.equals(monthYear)) {
                break;
            } else {
                clickOnElement(_nextMonthArrow);
            }

        }

        List<WebElement> allDates = driver.findElements(By.xpath("//body[1]/div[3]/div[1]/div[2]/table[1]/tbody[1]/tr/td"));

        for (WebElement ele : allDates) {
            String expectedDate = ele.getText();
            if (expectedDate.equals(date)) {
                ele.click();
                break;
            }
        }
    }

I've written a helper method to set the specified date. You create a LocalDate instance in the test and then pass that to the helper method and it will set the desired date in the date picker.

In the test

String url = "https://www.grangehotels.com/";
driver.get(url);

WebDriverWait wait = new WebDriverWait(driver, 10);
wait.until(ExpectedConditions.elementToBeClickable(By.cssSelector("#cookieConsent button"))).click();
wait.until(ExpectedConditions.elementToBeClickable(By.cssSelector("label.bookingmenu"))).click();
new Select(wait.until(ExpectedConditions.elementToBeClickable(By.id("Hotel")))).selectByVisibleText("Grange Buckingham Hotel");
wait.until(ExpectedConditions.elementToBeClickable(By.cssSelector("input[name='check_in_date']"))).click();

LocalDate checkInDate = LocalDate.of(2023, Month.MAY, 5);

SetDate(checkInDate);

The helper method

public static void SetDate(LocalDate targetDate) {
	// Get visible calendar TABLE
	WebDriverWait wait = new WebDriverWait(driver, 10);
	WebElement calendar = wait.until(ExpectedConditions.visibilityOfElementLocated(By.cssSelector("div.calendar-table > table")));

	// Move to target date panel
	DateTimeFormatter formatter = DateTimeFormatter.ofPattern("MMM yyyy");
	Boolean found = false;
	while (!found) {
		calendar = wait.until(ExpectedConditions.visibilityOfElementLocated(By.cssSelector("div.calendar-table > table")));
		String datePanel = calendar.findElement(By.cssSelector("th.month")).getText();

		// move right based on target date
		YearMonth datePanelLocalDate = YearMonth.parse(datePanel, formatter);
		int compareValue = datePanelLocalDate.compareTo(YearMonth.from(targetDate));
		if (compareValue == 0) {
			found = true;
		} else if (compareValue < 0) {
			driver.findElement(By.cssSelector("i.fa-chevron-right")).click();
		}
	}

	// Select day
	calendar.findElement(By.xpath(String.format(".//td[@class='available'][text()='%s']", targetDate.getDayOfMonth()))).click();
}

I didn't have your defined locators so I wrote my own. I've run this on the site several times and it's working as expected.