Clarify ISP proxies provide a static IP across sessions (#386)

* Clarify ISP proxies provide a static IP across sessions

ISP proxies are static both within a single browser session and across
separate sessions attached to the same proxy. Update the ISP page and
the overview info callout to reflect this and split datacenter (still
session-stable only) from ISP in the cross-type guidance.

* Correct datacenter proxy IP rotation behavior

Datacenter proxies rotate exit IPs per request, not per session. Update
the datacenter page and the overview info callout to reflect this.

* Apply suggestion from @dprevoznik

Author: dprevoznik

proxies/datacenter.mdx

@@ -6,9 +6,9 @@ Datacenter proxies use IP addresses assigned from datacenter servers to route yo
 
 ## IP Rotation Behavior
 
-Datacenter proxies provide a **stable exit IP within a single browser session** — every tab, request, and reconnection inside that session exits through the same IP, and it does not rotate mid-session (unlike residential).
+Datacenter proxies use **rotating exit IPs** — a new exit IP is assigned per request, so different requests within the same browser session can exit through different IPs.
 
-For cross-session IP stability (e.g. IP allowlists or [managed auth](/auth/overview) health checks), see [IP rotation behavior across proxy types](/proxies/overview).
+If you need a stable IP across requests and sessions (e.g. for IP allowlists or [managed auth](/auth/overview) health checks), use an [ISP proxy](/proxies/isp) instead. See [IP rotation behavior across proxy types](/proxies/overview) for the full comparison.
 
 ## Configuration
 

proxies/isp.mdx

@@ -6,9 +6,9 @@ ISP (Internet Service Provider) proxies are hosted on datacenter infrastructure
 
 ## IP Rotation Behavior
 
-ISP proxies provide a **stable exit IP within a single browser session** — every tab, request, and reconnection inside that session exits through the same IP, and it does not rotate mid-session (unlike residential).
+ISP proxies provide a **static exit IP that persists across sessions** — every tab, request, reconnection, and future browser session attached to this proxy exits through the same IP. The IP only changes in rare ISP-initiated replacement events.
 
-For cross-session IP stability (e.g. IP allowlists or [managed auth](/auth/overview) health checks), see [IP rotation behavior across proxy types](/proxies/overview).
+This makes ISP proxies suitable for use cases that require a stable IP, such as IP allowlists or [managed auth](/auth/overview) health checks. For comparison with other proxy types, see [IP rotation behavior across proxy types](/proxies/overview).
 
 ## Configuration
 

proxies/overview.mdx

@@ -16,7 +16,9 @@ Kernel supports four types of proxies:
 Datacenter has the fastest speed, while residential is least detectable. ISP is a balance between the two options, with less-flexible geotargeting. Kernel recommends to use the first option in the list that works for your use case.
 
 <Info>
-Datacenter and ISP proxies provide a **stable exit IP within a single browser session** — the IP does not rotate mid-session. Across separate sessions, however, Kernel does not guarantee the same exit IP. If you need a truly static IP that persists across every session (for example, an IP allowlist or a [managed auth](/auth/overview) connection whose health checks must egress from a single IP), use a [custom (BYO) proxy](/proxies/custom) pointed at infrastructure you control.
+ISP proxies provide a **static exit IP that persists across sessions** — every browser session attached to the proxy exits through the same IP, and it only changes in rare ISP-initiated replacement events. This makes them suitable for IP allowlists or [managed auth](/auth/overview) health checks that must egress from a single IP.
+
+Datacenter proxies use **rotating exit IPs** — a new exit IP is assigned per request, so different requests within the same browser session can exit through different IPs. For a stable IP across requests and sessions, use an ISP proxy or a [custom (BYO) proxy](/proxies/custom) pointed at infrastructure you control.
 
 Residential proxies use **rotating exit IPs** that may change per connection — see [Residential Proxies](/proxies/residential#ip-rotation-behavior) for details.
 </Info>