[Follow up to #8701] `NTP SI` is shown on 2nd attempt after browser launch, and then on every 4th instead of every 3rd attempt

[hffvld]

Description:

Follow-up to #8701

Steps to Reproduce

1. Install and launch Brave
2. Wait until landed on NTP
3. Open new NTP (2nd one in total) > Confirm that SI is opened
4. Open 4 more NTP > Observe that the next SI is shown on every 4th NTP

Actual result:

NTP SI is shown on the 2nd attempt after browser launch, and then on every 4th instead of every 3rd attempt.

1	2

https://github.com/brave/brave-ios/assets/128532965/db302e73-5da2-4191-8925-9659d0e503eb

Expected result:

As per https://github.com/brave/brave-ios/pull/8702#issue-2100748362:

• NTP SI is shown on 2nd NTP for BraveNTPBrandedWallpaper/initial_count_to_branded_wallpaper
• NTP SI is shown on every 3rd NTP for BraveNTPBrandedWallpaper/count_to_branded_wallpaper

Reproduces how often: [Easily reproduced, Intermittent Issue]

Easily reproduced

Brave Version:

Brave build: 1.62 (24.2.6.11)
BraveCore: 1.62.158 (121.0.6167.139)

• Can you reproduce this issue with the most recent build from TestFlight? YES
• Can you reproduce this issue with the previous version of the current build from TestFlight?
• Can you reproduce this issue with the current build from AppStore? YES

Device details:

iPhone 14 / iOS 17.4 Beta

Website problems only:

• did you check with Brave Shields down?
• did you check in Safari/Firefox (WkWebView-based browsers)?

Additional Information

[iccub]

@iambrianfung Hi is this behavior correct or a bug?

[iambrianfung]

i think @tmancey has some context. this should be correct behavior default behavior for ios, but possibly soon to change.